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Some cosmological models with non-negligible dark energy fractions in particular windows of the pre-recombination epoch are capable of alleviating the Hubble tension quite efficiently, while keeping the good description of the data that are used to build the cosmic inverse distance ladder. There has been an intensive discussion in the community on whether these models enhance the power of matter fluctuations, leading {\it de facto} to a worsening of the tension with the large-scale structure measurements. We address this pivotal question in the context of several early dark energy (EDE) models, considering also in some cases a coupling between dark energy and dark matter, and the effect of massive neutrinos. We fit them using the Planck 2018 likelihoods, the supernovae of Type Ia from the Pantheon compilation and data on baryon acoustic oscillations. We find that ultra-light axion-like (ULA) EDE can actually alleviate the $H_0$ tension without increasing the values of $\sigma_{12}$ with respect to those found in the $\Lambda$CDM, whereas EDE with an exponential potential does not have any impact on the tensions. A coupling in the dark sector tends to enhance the clustering of matter, and the data limit a lot the influence of massive neutrinos, since the upper bounds on the sum of their masses are too close to those obtained in the standard model. We find that in the best case, namely ULA, the Hubble tension is reduced to $\sim 2\sigma$., Comment: 27 pages, 16 figures, 8 tables. Version accepted for publication in Phys. Rev. D

A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on a one-dimensional lattice are equivalent to two - dimensional quantum field theories for fermions. They can be viewed as generalized Ising models on a square lattice and therefore as classical statistical systems. As quantum field theories they are quantum systems. Thus quantum mechanics emerges from classical statistics. As an explicit example for an interacting fermionic quantum field theory we describe a type of discretized Thirring model as a cellular automaton. The updating rule of the automaton is encoded in the step evolution operator that can be expressed in terms of fermionic annihilation and creation operators. The complex structure of quantum mechanics is associated to particle -- hole transformations. The naive continuum limit exhibits Lorentz symmetry. We exploit the equivalence to quantum field theory in order to show how quantum concepts as wave functions, density matrix, non-commuting operators for observables and similarity transformations are convenient and useful concepts for the description of probabilistic cellular automata., Comment: Clearer structure with focus on key points and appendices, 46 pages, 4 figures

We compute scaling solutions of functional flow equations for quantum gravity in a general truncation with up to four derivatives of the metric. They connect the asymptotically free ultraviolet fixed point, which is accessible to perturbation theory, to the non-perturbative infrared region. The existence of such scaling solutions is necessary for a renormalizable quantum field theory of gravity. If the proposed scaling solution is confirmed beyond our approximations asymptotic freedom is a viable alternative to asymptotic safety for quantum gravity., Comment: 19 pages, 10 figures, version published in JHEP

A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically on bit configurations. The genuinely probabilistic character of quantum physics is realized by probabilistic initial conditions. In turn, the probabilistic automaton is equivalent to the classical statistical system of a generalized Ising model. For a description of the probabilistic information at any given time quantum concepts as wave functions and non-commuting operators for observables emerge naturally. Quantum mechanics can be understood as a particular case of classical statistics. This offers prospects to realize aspects of quantum computing in the form of probabilistic classical computing., 15 pages, 1 figure

Models of inflationary cosmology admit a choice of the metric for which the geometry of homogeneous isotropic solutions becomes flat Minkowski space in the infinite past. In this primordial flat frame all mass scales vanish in the infinite past and quantum scale symmetry is realized. The cosmological evolution is dominantly described by the slow increase of a scalar field which sets the scale of all masses. We construct the primordial flat frame for standard models of inflation as Starobinsky inflation or chaotic inflation. In particular, we discuss the evolution of inhomogeneous solutions in the neighborhood of the homogeneous isotropic background solution and their relation to the observable primordial fluctuation spectrum. If the propagators for the graviton and scalar field remain regular, our observed inhomogeneous Universe can be extrapolated back to the infinite past in physical time. In this case there is no physical big-bang singularity -- the latter reflects only a singular choice of ``field coordinates". Independently of the issue of singularity the primordial flat frame offers a new view on the physical properties of the inflationary universe, which can be characterized as a very slowly evolving almost empty vacuum state with approximate scale symmetry., additional discussion of inhomogeneous cosmological solutions and big bang singularity , 31 pages

We discuss cosmological solutions for a diffeomorphism invariant gauge theory of the non-compact Lorentz group $SO(1,3)$. Besides the gauge bosons our model of pregeometry contains a vector field in the vector representation of $SO(1,3)$ and a scalar singlet. General relativity and variable gravity emerge as effective theories for large distances and times in Planck units. We propose an approximation to the effective action with up to two derivatives. For a suitable range of parameters the universe approaches for large times stable Minkowski space. For late cosmology the model predicts dynamical dark energy and provides for a candidate for dark matter. Early cosmology is characterized by an inflationary epoch. The beginning of the universe in the infinite past is great emptiness, corresponding to an ultraviolet fixed point with the associated quantum scale symmetry. The beginning universe is a vacuum state with vanishing expectation values and finite non-vanishing correlation functions for the fluctuations of all fields. There is no physical big bang singularity., Comment: Further explanations, new references, 63 pages, 9 figures

In pregeometry a metric arises as a composite object at large distances. We investigate if its signature, which distinguishes between time and space, could be a result of the dynamics rather than being built in already in the formulation of a model. For short distances we formulate our model as a Yang-Mills theory with fermions and vector fields. For the local gauge symmetry we take the non-compact group SO(4,\,$\mathbb{C}$). The particular representation of the vector field permits us to implement diffeomorphism invariant kinetic terms. Geometry and general relativity emerge at large distances due to a spontaneous breaking of the gauge symmetry which induces masses for the gauge bosons. The difference between time and space arises directly from this spontaneous symmetry breaking. For a euclidean metric all fields have a standard propagator at high momenta. Analytic continuation to a Minkowski-metric is achieved by a change of field values. We conjecture that this type of model could be consistent with unitarity and well behaved in the short distance limit., Comment: Extended discussion of the role of quantum fluctuations, 28 pages

Inflation and quintessence can both be described by a single scalar field. The cosmic time evolution of this cosmon field realizes a crossover from the region of an ultraviolet fixed point in the infinite past to an infrared fixed point in the infinite future. This amounts to a transition from early inflation to late dynamical dark energy, with intermediate radiation and matter domination. The scaling solution of the renormalization flow in quantum gravity connects the two fixed points. It provides for the essential characteristics of the scalar potential needed for the crossover cosmology and solves the cosmological constant problem dynamically. The quantum scale symmetry at the infrared fixed point protects the tiny mass of the cosmon and suppresses the cosmon coupling to atoms without the need of a non-linear screening mechanism, thereby explaining apparent issues of fine tuning. For a given content of particles the scaling solution of quantum gravity is a predictive framework for the properties of inflation and dynamical dark energy., Comment: 13 pages, 2 figures

Partial bosonization of the two-dimensional Hubbard model focuses the functional renormalization flow on channels in which interactions become strong and local order sets in. We compare the momentum structure of the four-fermion vertex, obtained on the basis of a patching approximation, to an effective bosonic description. For parameters in the antiferromagnetic phase near the onset of local antiferromagnetic order, the interaction of the electrons is indeed well described by the exchange of collective bosonic degrees of freedom. The residual four-fermion vertex after the subtraction of the bosonic-exchange contribution is small. We propose that similar partial bosonization techniques can improve the accuracy of renormalization flow studies also for the case of competing order.

We propose that neuromorphic computing can perform quantum operations. Spiking neurons in the active or silent states are connected to the two states of Ising spins. A quantum density matrix is constructed from the expectation values and correlations of the Ising spins. As a step towards quantum computation we show for a two qubit system that quantum gates can be learned as a change of parameters for neural network dynamics. Our proposal for probabilistic computing goes beyond Markov chains, which are based on transition probabilities. Constraints on classical probability distributions relate changes made in one part of the system to other parts, similar to entangled quantum systems., Comment: 9 pages, 8 figures

A general prediction from asymptotically safe quantum gravity is the approximate vanishing of all quartic scalar couplings at the UV fixed point beyond the Planck scale. A vanishing Higgs doublet quartic coupling near the Planck scale translates into a prediction for the ratio between the mass of the Higgs boson $M_H$ and the top quark $M_t$. If only the standard model particles contribute to the running of couplings below the Planck mass, the observed $M_H\sim125\,{\rm GeV}$ results in the prediction for the top quark mass $M_t\sim 171\,{\rm GeV}$, in agreement with recent measurements. In this work, we study how the asymptotic safety prediction for the top quark mass is affected by possible physics at an intermediate scale. We investigate the effect of a $SU(2)$ triplet scalar and right-handed neutrinos, needed to explain the tiny mass of left-handed neutrinos. For pure seesaw II, with no or very heavy right handed neutrinos, the top mass can increase to $M_t\sim 172.5\,{\rm GeV}$ for a triplet mass of $M_\Delta\sim 10^8{\rm GeV}$. Right handed neutrino masses at an intermediate scale increase the uncertainty of the predictions of $M_t$ due to unknown Yukawa couplings of the right-handed neutrinos and a cubic interaction in the scalar potential. For an appropriate range of Yukawa couplings there is no longer an issue of vacuum stability., Comment: 18 pages, 16 figures

Asymptotically safe quantum fluctuations of gravity can uniquely determine the value of the gauge coupling for a large class of grand unified models. In turn, this makes the electromagnetic fine-structure constant calculable. The balance of gravity and matter fluctuations results in a fixed point for the running of the gauge coupling. It is approached as the momentum scale is lowered in the transplanckian regime, leading to a uniquely predicted value of the gauge coupling at the Planck scale. The precise value of the predicted fine-structure constant depends on the matter content of the grand unified model. It is proportional to the gravitational fluctuation effects for which computational uncertainties remain to be settled., Comment: 4 pages plus references, 2 figures

Using the gauge invariant flow equation for quantum gravity we compute how the strength of gravity depends on the length or energy scale. The fixed point value of the scale-dependent Planck mass in units of the momentum scale has an important impact on the question, which parameters of the Higgs potential can be predicted in the asymptotic safety scenario for quantum gravity? For the standard model and a large class of theories with additional particles the quartic Higgs coupling is an irrelevant parameter at the ultraviolet fixed point. This makes the ratio between the Higgs boson and the top-quark mass predictable., 43 pages, 11 figures, version published in PRD

In the wake of interest to find black hole solutions with scalar hair, we investigate the effects of disformal transformations on static spherically symmetric spacetimes with a nontrivial scalar field. In particular, we study solutions that have a singularity in a given frame, while the action is regular. We ask if there exists a different choice of field variables such that the geometry and the fields are regular. We find that in some cases disformal transformations can remove a singularity from the geometry or introduce a new horizon. This is possible since the Weyl tensor is not invariant under a general disformal transformation. There exists a class of metrics which can be brought to Minkowksi geometry by a disformal transformation, which may be called disformally flat metrics. We investigate three concrete examples from massless scalar fields to Horndeski theory for which the singularity can be removed from the geometry. This might indicate that no physical singularity is present. We also propose a disformal invariant tensor.

Am Anfang des Universums war fast nichts –Vakuum mit nur seltenen Elementarteilchen, die sich mit Lichtgeschwindigkeit bewegten. Erst spater wurde das Plasma aus Elementarteilchen erzeugt, das unserem gangigen Urknallbild zugrunde liegt. Wie lange diese Anfangsperiode dauerte, hangt vom Konzept der Zeit ab. „Physikalische Uhren“ tickten unendlich oft, das Universum gab es schon immer. Nur in der unphysikalischen „Eigenzeit“ schrumpft die Anfangsperiode auf winzige Bruchteile von Sekunden zusammen.

A single paragraph of about 200 words maximum. For research articles, abstracts should give a pertinent overview of the work. We strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: place the question addressed in a broad context and highlight the purpose of the study, (2) Methods: describe briefly the main methods or treatments applied, (3) Results: summarize the article’s main findings, (4) Conclusion: indicate the main conclusions or interpretations. The abstract should be an objective representation of the article, it must not contain results which are not presented and substantiated in the main text and should not exaggerate the main conclusions.

We investigate the dimensional crossover from three to two dimensions in an ultracold Fermi gas across the whole BCS-BEC crossover. Of particular interest is the strongly interacting regime as strong correlations are more pronounced in reduced dimensions. Our results are obtained from first principles within the framework of the functional renormalisation group (FRG). Here, the confinement of the transverse direction is imposed by means of periodic boundary conditions. We calculate the equation of state, the gap parameter at zero temperature and the superfluid transition temperature across a wide range of transversal confinement length scales. Particular emphasis is put on the determination of the finite temperature phase diagram for different confinement length scales. In the end, our results are compared with recent experimental observations and we discuss them in the context of other theoretical works., Comment: 23 pages, 12 figures; additional explanations and comments, corrected typos, new and updated references; very close to published version

We explore the infrared limit of quantum gravity in presence of a cosmological constant or effective potential for scalar fields. For a positive effective scalar potential, one-loop perturbation theory around flat space is divergent due to an instability of the graviton propagator. Functional renormalization solves this problem by a flow of couplings avoiding instabilities. This leads to a graviton barrier limiting the maximal growth of the effective potential for large values of scalar fields. In the presence of this barrier, variable gravity with a field dependent Planck mass can solve the cosmological constant problem by a cosmological runaway solution. We discuss the naturalness of tiny values of the cosmological constant and cosmon mass due to a strong attraction towards an infrared fixed point., Comment: new references, 9 pages , 3 figures

Primordial black holes can be produced by a long range attractive fifth force stronger than gravity, mediated by a light scalar field interacting with nonrelativistic "heavy" particles. As soon as the energy fraction of heavy particles reaches a threshold, the fluctuations rapidly become nonlinear. The overdensities collapse into black holes or similar screened objects, without the need for any particular feature in the spectrum of primordial density fluctuations generated during inflation. We discuss whether such primordial black holes can constitute the total dark matter component in the Universe., Comment: 6 pages, 1 figure, published version, added clarifications and references, corrected typos

A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level observables, and the quantum subsystem employs suitable expectation values and correlations. We discuss static memory materials based on Ising spins for which boundary information can be transported through the bulk in a generalized equilibrium state. They can realize quantum operations as the Hadamard or CNOT-gate for the quantum subsystem. Classical probabilistic systems can account for the entanglement of quantum spins. An arbitrary unitary evolution for an arbitrary number of quantum spins can be described by static memory materials for an infinite number of Ising spins which may, in turn, correspond to continuous variables or fields. We discuss discrete subsets of unitary operations realized by a finite number of Ising spins. They may be useful for new computational structures. We suggest that features of quantum computation or more general probabilistic computation may be realized by neural networks, neuromorphic computing or perhaps even the brain. This does neither require small isolated entities nor very low temperature. In these systems the processing of probabilistic information can be more general than for static memory materials. We propose a general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases., Comment: New discussion of Bells inequalities and no cloning theorem for classical probabilistic systems, 51 pages, 3 figures

The effect of gravitational fluctuations on the quantum effective potential for scalar fields is a key ingredient for predictions of the mass of the Higgs boson, understanding the gauge hierarchy problem and a possible explanation of an---asymptotically---vanishing cosmological constant. We find that the quartic self-interaction of the Higgs scalar field is an irrelevant coupling at the asymptotically safe ultraviolet fixed point of quantum gravity. This renders the ratio between the masses of the Higgs boson and top quark predictable. If the flow of couplings below the Planck scale is approximated by the Standard Model, this prediction is consistent with the observed value. The quadratic term in the Higgs potential is irrelevant if the strength of gravity at short distances exceeds a bound that is determined here as a function of the particle content. In this event, a tiny value of the ratio between the Fermi scale and the Planck scale is predicted., Comment: 18 pages, 5 figures, Version published in PRD

We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of products of observables. The map preserves locality properties and can be realized for arbitrary dimensions. We present a simple example where a quantum field theory for free massless Dirac fermions in two-dimensional Minkowski space is represented by an asymmetric Ising model on a euclidean square lattice., small changes, 17 pages

In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg picture for this problem, we develop here the associated Schr\"odinger picture that keeps track of the local probabilistic information. The transport of the probabilistic information between neighboring hypersurfaces obeys a linear evolution equation, and therefore the superposition principle for the possible solutions. Operators are associated to local observables, with rules for the computation of expectation values similar to quantum mechanics. We discuss how non-commutativity naturally arises in this setting. Also other features characteristic of quantum mechanics, such as complex structure, change of basis or symmetry transformations, can be found in classical statistics once formulated in terms of wave functions or density matrices. We construct for every quantum system an equivalent classical statistical system, such that time in quantum mechanics corresponds to the location of hypersurfaces in the classical probabilistic ensemble. For suitable choices of local observables in the classical statistical system one can, in principle, compute all expectation values and correlations of observables in the quantum system from the local probabilistic information of the associated classical statistical system. Realizing a static memory material as a quantum simulator for a given quantum system is not a matter of principle, but rather of practical simplicity., Comment: New section with example of three-spin chain realising quantum gates, 53 pages. arXiv admin note: text overlap with arXiv:1611.04820

We derive a new exact evolution equation for the scale dependence of an effective action. The corresponding equation for the effective potential permits a useful truncation. This allows one to deal with the infrared problems of theories with massless modes in less than four dimensions which are relevant for the high temperature phase transition in particle physics or the computation of critical exponents in statistical mechanics., Comment: Original manuscript from 1992, 5 pages

Linear lattice gauge theory is based on link variables that are arbitrary complex or real $N\times N$ matrices, in distinction to the usual (non-linear) formulation with unitary or orthogonal matrices. For a large region in parameter space both formulations belong to the same universality class, such that the continuum limits of linear and non-linear lattice gauge theory are identical. We explore if the linear formulation can help to find a non-perturbative continuum limit formulated in terms of continuum fields. Linear lattice gauge theory exhibits excitations beyond the gauge fields. In the linear formulation the running gauge coupling corresponds to the flow of the minimum of a ``link potential''. This minimum occurs for a nonzero value of the link variable $l_0$ in the perturbative regime, while $l_0$ vanishes in the confinement regime. We discuss a flow equation for the scale dependent location of the minimum $l_0(k)$., Comment: extended discussion of relation to standard gauge theories, 13 pages. arXiv admin note: substantial text overlap with arXiv:1212.3507

We investigate the formation and dissipation of large scale neutrino structures in cosmologies where the time evolution of dynamical dark energy is stopped by a growing neutrino mass. In models where the coupling between neutrinos and dark energy grows with the value of the scalar cosmon field, the evolution of neutrino lumps depends on the neutrino mass. For small masses the lumps form and dissolve periodically, leaving only a small backreaction of the neutrino structures on the cosmic evolution. This process heats the neutrinos to temperatures much above the photon temperature such that neutrinos acquire again an almost relativistic equation of state. The present equation of state of the combined cosmon-neutrino fluid is very close to -1. In contrast, for larger neutrino masses the lumps become stable. The highly concentrated neutrino structures entail a large backreaction similar to the case of a constant neutrino-cosmon coupling. A present average neutrino mass of around 0.5 eV seems so far compatible with observation. For masses lower than this value, neutrino induced gravitational potentials remain small, making the lumps difficult to detect., 19 pages, 10 figures, 3 tables

We explore models with emergent gravity and metric by means of numerical simulations. A particular type of two-dimensional non-linear sigma-model is regularized and discretized on a quadratic lattice. It is characterized by lattice diffeomorphism invariance which ensures in the continuum limit the symmetry of general coordinate transformations. We observe a collective order parameter with properties of a metric, showing Minkowski or euclidean signature. The correlation functions of the metric reveal an interesting long-distance behavior with power-like decay. This universal critical behavior occurs without tuning of parameters and thus constitutes an example of "self-tuned criticality" for this type of sigma-models. We also find a non-vanishing expectation value of a "zweibein" related to the "internal" degrees of freedom of the scalar field, again with long-range correlations. The metric is well described as a composite of the zweibein. A scalar condensate breaks euclidean rotation symmetry., 22 pages, 17 figures, Nucl. Phys. B version, minor changes

We investigate how confining a transverse spatial dimension influences the few- and many-body properties of non-relativistic bosons with pointlike interactions. Our main focus is on the dimensional crossover from three to two dimensions, which is of relevance for ultracold atom experiments. Using Functional Renormalization Group equations and T-matrix calculations we study how the phase transition temperature changes as a function of the spatial extent of the transverse dimension and relate the 3D and 2D s-wave scattering lengths. The analysis reveals how the properties of the lower-dimensional system are inherited from the higher-dimensional one during the renormalization group evolution. We limit the discussion to confinements in a potential well with periodic boundary conditions and argue why this qualitatively captures the physics of other compactifications such as transverse harmonic confinement as in cold atom experiments., Comment: 17 pages

We discuss the correlation function for the metric for homogeneous and isotropic cosmologies. The exact propagator equation determines the correlation function as the inverse of the second functional derivative of the quantum effective action. This formulation relates the metric correlation function employed in quantum gravity computations to cosmological observables as the graviton power spectrum. In the Einstein-Hilbert approximation for the effective action the on-shell graviton correlation function can be obtained equivalently from a product of mode functions which solve the linearized Einstein equations. In contrast, the product of mode functions, often employed in the context of cosmology, does not yield the correlation function for the vector and scalar components of the metric fluctuations. We divide the metric fluctuations into "physical fluctuations", which couple to a conserved energy momentum tensor, and gauge fluctuations. On the subspace of physical metric fluctuations the relation to physical sources becomes invertible, such that the effective action and its relation to correlation functions no longer needs to involve a gauge fixing term. The physical metric fluctuations have a similar status as the Bardeen potentials, while being formulated in a covariant way. We compute the effective action for the physical metric fluctuations for geometries corresponding to realistic cosmologies., Comment: extended discussion of off-shell propagator and mode functions, new references, 38 pages

We argue that the chemical freeze-out in heavy ion collisions at high baryon density is not associated to a phase transition or rapid crossover. We employ the linear nucleon-meson model with parameters fixed by the zero-temperature properties of nuclear matter close to the liquid-gas quantum phase transition. For the parameter region of interest this yields a reliable picture of the thermodynamic and chiral properties at non-zero temperature. The chemical freeze-out observed in low-energy experiments occurs when baryon densities fall below a critical value of about 15 percent of nuclear density. This region in the phase diagram is far away from any phase transition or rapid crossover., Comment: 8 pages, 11 figures, published version

Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space and time is not put in a priori, and the euclidean and Minkowski quantum field theory are unified in one functional integral. The metric and its signature arise as a result of the dynamics, corresponding to a given ground state or cosmological solution. Geometrical objects as the vierbein, spin connection or the metric are expectation values of collective fields built from an even number of fermions. The quantum effective action for the metric is invariant under general coordinate transformations in the continuum limit. The action of our model is found to be also invariant under gauge transformations. We observe a "geometrical entanglement" of gauge- and Lorentz-transformations due to geometrical objects transforming non-trivially under both types of symmetry transformations., Comment: 38 pages

The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions $p_\tau(t)$ at a given time $t$ obtain by integrating out the past and future. We discuss all-time probability distributions that realize a unitary time evolution as described by rotations of the real wave function $q_\tau(t)=\pm \sqrt{p_\tau(t)}$. We establish a map to quantum physics and the Schr\"odinger equation. Suitable classical observables are mapped to quantum operators. The non-commutativity of the operator product is traced back to the incomplete statistics of the local-time subsystem. Our investigation of classical statistics is based on two-level observables that take the values one or zero. Then the wave functions can be mapped to elements of a Grassmann algebra. Quantum field theories for fermions arise naturally from our formulation of probabilistic time., Comment: new references, 30 pages

We describe both quantum particles and classical particles in terms of a classical statistical ensemble, characterized by a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same quantum formalism. The different dynamics of quantum and classical particles resides then only from different evolution equations for the probability distribution. Quantum particles are characterized by a specific choice of observables and time evolution of the probability density. All relations for a quantum particle in a potential, including interference and tunneling, can be described in terms of the classical probability distribution. We formulate the concept of zwitters - particles for which the time evolution interpolates between quantum and classical particles. Experiments can test a small parameter which quantifies possible deviations from quantum mechanics., Comment: extended discussion of possible realizations of zwitters, including macroscopic droplets or BEC condensates

We discuss fermions for arbitrary dimensions and signature of the metric, with special emphasis on euclidean space. Generalized Majorana spinors are defined for $d=2,3,4,8,9$ mod 8, independently of the signature. These objects permit a consistent analytic continuation of Majorana spinors in Min-kowski space to euclidean signature. Compatibility of charge conjugation with complex conjugation requires for euclidean signature a new complex structure which involves a reflection in euclidean time. The possible complex structures for Minkowski and euclidean signature can be understood in terms of a modulo two periodicity in the signature. The concepts of a real action and hermitean observables depend on the choice of the complex structure. For a real action the expectation values of all hermitean multi-fermion observables are real. This holds for arbitrary signature, including euclidean space. In particular, a chemical potential is compatible with a real action for the euclidean theory. We also discuss the discrete symmetries of parity, time reversal and charge conjugation for arbitrary dimension and signature., Comment: extended version, detailed discussion of four-dimensional euclidean Majorana spinors, extended descripton of complex structures, discussion of chemical potential for euclidean fermions and reality of action, 70 pages

We describe fermions in terms of a classical statistical ensemble. The states $\tau$ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability distribution can be associated to a quantum state for fermions. If the time evolution of the classical probabilities $p_\tau$ amounts to a rotation of the wave function $q_\tau(t)=\pm \sqrt{p_\tau(t)}$, we infer the unitary time evolution of a quantum system of fermions according to a Schr\"odinger equation. We establish how such classical statistical ensembles can be mapped to Grassmann functional integrals. Quantum field theories for fermions arise for a suitable time evolution of classical probabilities for generalized Ising models., Comment: extended version with two new sections on symmetries 25 pages

Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs, however, between quantum and classical particles. We describe position, motion and correlations of a quantum particle in terms of observables in a classical statistical ensemble. On the other side, we also construct explicitly the quantum formalism with wave function and Hamiltonian for classical particles. For a suitable time evolution of the classical probabilities and a suitable choice of observables all features of a quantum particle in a potential can be derived from classical statistics, including interference and tunneling. Besides conceptual advances, the treatment of classical and quantum particles in a common formalism could lead to interesting cross-fertilization between classical statistics and quantum physics., Comment: New material on quantum formalism and wave function for classical particles. Part of previous material is moved to a separate paper. 25 pages

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a "purity constraint". Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer., Comment: 33 pages, improvement of presentation

Antisymmetric tensor fields interacting with quarks and leptons have been proposed as a possible solution to the gauge hierarchy problem. We compute the one-loop beta function for a quartic self-interaction of the chiral antisymmetric tensor fields. Fluctuations of the top quark drive the corresponding running coupling to a negative value as the renormalization scale is lowered. This may indicate a non-vanishing expectation value of the tensor field, and thus a spontaneous breaking of Lorentz invariance. Settling this issue will need the inclusion of tensor loops., Comment: 15 pages, 4 figures

Occupation numbers for non-relativistic interacting particles are discussed within a functional integral formulation. We concentrate on zero temperature, where the Bogoliubov theory breaks down for strong couplings as well as for low dimensional models. We find that the leading behavior of the occupation numbers for small momentum is governed by a quadratic time derivative in the inverse propagator that is not contained in the Bogoliubov theory. We propose to use a functional renormalization group equation for the occupation numbers in order to implement systematic non-perturbative extensions beyond the Bogoliubov theory., 20 pages

A growing neutrino mass can stop the dynamical evolution of a dark energy scalar field, thus explaining the 'why now' problem. We show that such models lead to a substantial neutrino clustering on the scales of superclusters. Nonlinear neutrino lumps form at redshift z \sim 1 and could partially drag the clustering of dark matter. If observed, large scale non-linear structures could be an indication for a new attractive 'cosmon force' stronger than gravity., 6 pages, 5 figures

A second rank antisymmetric tensor field is proposed as an alternative to the Higgs scalar. No mass term is allowed by the symmetries. At the scale where the asymptotically free chiral couplings of the fermions grow large, condensates of top-antitop and bottom-antibottom may induce the spontaneous breaking of the electroweak gauge symmetry. This would solve the gauge hierarchy problem by dimensional transmutation, similar to QCD., Comment: extended discussion of consistency and mass generation, 4 pages

The temperature dependence of d-wave superconducting order for two-dimensional fermions with d-wave attraction is investigated by means of the functional renormalization group with partial bosonization. Below the critical temperature T c we find superconductivity, a gap in the electron propagator and a temperature-dependent anomalous dimension. At T c the renormalized “superfluid density” jumps and the approach to T c from above is characterized by essential scaling. These features are characteristic for a phase transition of the Kosterlitz–Thouless (KT) type.

We investigate the cosmological effects of neutrino lumps in Growing Neutrino Quintessence. The strongly non-linear effects are resolved by means of numerical N-body simulations which include relativistic particles, non-linear scalar field equations and backreaction effects. For the investigated models with a constant coupling between the scalar field and the neutrinos the backreaction effects are so strong that a realistic cosmology is hard to realize. This points towards the necessity of a field dependent coupling in Growing Neutrino Quintessence. In this case realistic models of dynamical Dark Energy exist which are testable by the observation or non-observation of large neutrino lumps., 10 pages, 6 figures

We discuss the possibility of a dynamical solution to the cosmological constant problem in the contaxt of six-dimensional Einstein-Maxwell theory. A definite answer requires an understanding of the full bulk cosmology in the early universe, in which the bulk has time-dependent size and shape. We comment on the special properties of codimension two as compared to higher codimensions., 11 pages

We argue that hadron multiplicities in central high energy nucleus-nucleus collisions are established very close to the phase boundary between hadronic and quark matter. In the hadronic picture this can be described by multi-particle collisions whose importance is strongly enhanced due to the high particle density in the phase transition region. As a consequence of the rapid fall-off of the multi-particle scattering rates the experimentally determined chemical freeze-out temperature is a good measure of the phase transition temperature., final version, some comments added about "statistical hadronization", to appear in Phys. Lett. B

Quintessence -- the energy density of a slowly evolving scalar field -- may constitute a dynamical form of the homogeneous dark energy in the universe. We review the basic idea in the light of the cosmological constant problem. Cosmological observations or a time variation of fundamental `constants' can distinguish quintessence from a cosmological constant., 6 pages, 2 figures, contribution to Dark Matter 2002

We examine the cosmic microwave background (CMB) anisotropy for signatures of early quintessence dark energy -- a non-negligible quintessence energy density during the recombination and structure formation eras. Only very recently does the quintessence overtake the dark matter and push the expansion into overdrive. Because the presence of early quintessence exerts an influence on the clustering of dark matter and the baryon-photon fluid, we may expect to find trace signals in the CMB and the mass fluctuation power spectrum. In detail, we demonstrate that suppressed clustering power on small length-scales, as suggested by the combined Wilkinson Microwave Anisotropy Probe (WMAP) / CMB / large scale structure data set, is characteristic of early quintessence. We identify a set of concordant models, and map out directions for further investigation of early quintessence.

The instanton interaction in QCD generates an effective potential for scalar quark–antiquark condensates in the color singlet and octet channels. For three light quark flavors the cubic term in this potential induces an octet condensate and may lead to “spontaneous breaking” of color in the vacuum. Realistic masses of the ρ- and η′-mesons are compatible with renormalization-group-improved instanton perturbation theory.

Quintessence - the energy density of a slowly evolving scalar field - may constitute a dynamical form of the homogeneous dark energy in the universe. We review the basic idea and indicate observational tests which may distinguish quintessence from a cosmological constant.

The distinction between modified gravity and quintessence or dynamical dark energy is difficult. Many models of modified gravity are equivalent to models of coupled quintessence by virtue of variable transformations. This makes an observational differentiation between modified gravity and dark energy very hard. For example, the additional scalar degree of freedom in f(R)-gravity or non-local gravity can be interpreted as the cosmon of quintessence. Nevertheless, modified gravity can shed light on questions of interpretation, naturalness and simplicity. We present a simple model where gravity is modified by a field dependent Planck mass. It leads to a universe with a cold and slow beginning. This cosmology can be continued to the infinite past such that no big bang singularity occurs. All observables can be described equivalently in a hot big bang picture with inflation and early dark energy.