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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

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

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 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 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

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 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

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

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 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

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.

We discuss first order transitions for systems in the Ising universality class. The critical long distance physics near the endpoint of the critical line is explicitly connected to microscopic properties of a given system. Information about the short distance physics can therefore be extracted from the precise location of the endpoint and non-universal amplitudes. Our method is based on non-perturbative flow equations and yields directly the universal features of the equation of state, without additional theoretical assumptions of scaling or resummations of perturbative series. The universal results compare well with other methods., LaTeX, 22 pages with 7 figures, uses epsf.sty and rotate.sty

The QCD-vacuum is characterized by the Higgs phenomenon for colored scalar fields. In this dual picture the gluons appear as the octet of vector mesons. Also quarks and baryons are identified. Gluon-meson and quark-baryon duality can account in a simple way for realistic masses of all low-mass hadrons and for their interactions., 7 pages

The naturalness of maximal mixing between myon- and tau-neutrinos is investigated. A spontaneously broken nonabelian generation symmetry can explain a small parameter which governs the deviation from maximal mixing. In many cases all three neutrino masses are almost degenerate. Maximal ν μ − ν τ -mixing suggests that the leading contribution to the light neutrino masses arises from the expectation value of a heavy weak triplet rather than from the seesaw mechanism. In this scenario the deviation from maximal mixing is predicted to be less than about 1%.

The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show that this fixed point is not universally stable, since infinitely many conserved correlation functions obstruct the approach to equilibrium. Equilibrium can therefore be reached at most for suitably averaged quantities or for subsystems, similar to quantum statistics. The classical time evolution of correlation functions shows many dynamical features of quantum mechanics., Comment: 13 pages, LaTeX

A quantitative discussion of nonperturbative effects for the high temperature electroweak phase transition is presented. We propose a method for the computation of the temperature dependent effective scalar potential that takes into account the running of the effective gauge coupling. Compared to perturbation theory we find a moderate decrease of the critical temperature and an important change in the strength of the first order transition. We conclude that perturbation theory gives a misleading picture of the dynamics of the transition., Comment: 17 pages + 5 ps-figures, LaTeX

We explore the Coleman-Weinberg phase transition in regions outside the validity of perturbation theory. For this purpose we study a Euclidean field theory with two scalars and discrete symmetry in four dimensions. The phase diagram is established by a numerical solution of a suitable truncation of exact non-perturbative flow equations. We find regions in parameter space where the phase transition (in dependence on the mass term) is of the second or the first order, separated by a triple point. Our quantitative results for the first order phase transition compare well to the standard perturbative Coleman-Weinberg calculation of the effective potential., Comment: 14 pages, Oxford OUTP 94-14 P, Heidelberg HD-THEP-94-15

Within the Euclidean effective action approach we propose criteria for the ground state of QCD. Despite a nonvanishing field strength the ground state should be invariant with respect to modified Poincar\'e transformations consisting of a combination of translations and rotations with suitable gauge transformations. We have found candidate states for QCD with four or more colours. The formation of gluon condensates shows similarities with the Higgs phenomenon., Comment: 17 pages, latex, DESY 94-081, HD-THEP-94-6

Evolution equations describe the effect of consecutively integrating out all quantum fluctuations with momenta larger than some infrared cutoff scale k. We develop a formalism for the introduction of collective degrees of freedom at some intermediate scale and derive the corresponding evolution equations. This allows to account for the appearance of bound states at some characteristic length scale as, for example, the mesons in QCD. The vacuum properties, including condensates of composite operators, can be directly infered from the effective action for k->0. We compute in a simple QCD-motivated model with four-quark interactions the chiral condensate \bar\psi\psi and the effective action for pions including f_\pi. A full treatment of QCD along these lines seems feasible but still requires substantial work. (5 figures available by ordinary mail upon request), Comment: 31 pages, HD-THEP-94-1

We propose a new nonperturbative evolution equation for Yang-Mills theories. It describes the scale dependence of an effective action. The running of the nonabelian gauge coupling in arbitrary dimension is computed.

We present a method which allows us to deal with the strong infrared effects in three-dimensional gauge theories. In particular, we compute the three-dimensional running of the gauge coupling. Applying these results to the electroweak phase transition in the standard model, we conclude that the transition cannot be of second order. It is either a first-order transition or a smooth cross-over.

We investigate the temperature dependent effective potential for N -component φ 4 theories with a new method based on averages of fields. The effective three-dimensional running of couplings at scales much below the temperature is described. We obtain a detailed quantitative picture of the second order phase transition, including the critical exponents for the behaviour in the vicinity of the critical temperature.

We show how geometrical quantities as distance, topology and riemannian metric can be constructed from the correlation functions in general statistical systems.

We develop the concept of an average action for gauge theories in the continuum. The average scalar potential of the abelian Higgs model is computed in arbitrary dimensions.

The average potential describes the physics at a length scale k −1 by averaging out the degrees of freedom with characteristic momenta larger than k . The dependence on k can be described by differential evolution equations. We solve these equations for the non-convex part of the potential around the origin in φ 4 theories, in the phase with spontaneous symmetry breaking. The average potential is real and approaches the convex effective potential in the limit k → 0. Our calculation is relevant for processes for which the shape of the potential at a given scale is important, such as tunneling phenomena or inflation.

Fermions and scalars contribute with opposite sign to the dependence of the scalar mass term m2 on the length scale k−1. We discuss the possibility that a “balance effect” between these contributions leads to an infrared stable fixed point in the evolution of the ratio m2(k)/k2. Such a behavior would result in self-organizing criticality and could naturally explain a small gauge hierarchy. It is closely related to a large anomalous mass dimension.

We investigate the experimental signatures of the recently proposed “geometrical” production of many W, Z, Higgs and (primordial) fermions ( n w ≈ α w −1 ≈ 30) with a relatively large cross section. We believe that such events, if they exist, stand a very good chance to be seen at the LHC (SSC) provided that the (parton) threshold energy for the onset of geometrical flavour production is below 11 (28) TeV.

At very high energies the mean particle multiplicity in electroweak scattering processes should become high, associated with slowly raising total inelastic cross sections. I speculate that this nonperturbative phenomenon may already occur for energies above a few TeV.

Weak interactions at high energies (√ s ⩾ m w / α w ) may lead to strong multiparticle production of weakly interacting particles. This effect is connected to infrared divergences of the underlying gauge theory. Cross sections for the production of many weakly interacting particles of the order 1 nb to 10 μb above a threshold (parton) energy of 2 to 20 TeV could be observable at future colliders.

It is shown that the existence of gauge hierarchies in unified theories of strong, weak and electromagnetic interactions permits unification of the three forces at energies as high as Planck mass. As examples, we discuss the O(10), E 6 and [SU(4)] 4 models. Implications for proton decay and for present and future weak intermediate boson phenomenology are considered.

We show how chiral four-dimensional spinors can be obtained from six-dimensional riemannian geometry, if two dimensions form a noncompact internal space with finite volume.

We examine patterns where ratios of the fermion masses and the W-boson mass ( x i = m i m w ) are proportional to powers of a small parameter λ(xi=ciλPi). For a simple estimate of the uncertainty in the coefficients ci we determine the allowed values of Pi and the corresponding range of λ. Using this information we search for realistic patterns in a large class of anomaly-free SU(3)×SU(2)×U(1)×U(1) models where λ is related to a symmetry breaking scale and the Pi follow from the quantum numbers. No realistic model is found. In contrast, realistic mass patterns can be induced from an anomalous U(1) symmetry.

Einstein's equations with a cosmological constant in arbitrary dimensions admit solutions with unobservable internal space and flat four-dimensional space. Internal space is non-compact, has finite volume and admits a compact group of symmetries. No fine tuning of parameters is needed to obtain a vanishing four-dimensional cosmological constant.

The number of chiral fermions may change in the course of spontaneous symmetry breaking. We discuss solutions of a six-dimensional Einstein-Yang-Mills theory based on SO(12). In the resulting effective four-dimensional theory they can be interpreted as spontaneous breaking of a gauge group SO(10) to H = SU (3) C × SU (2) L × U (1) R × U (10) B−L . For all solutions, the fermions which are chiral with respect to H form standard generations. However, the number of generations for the solutions with broken SO(10) may be different compared to the symmetric solutions. All solutions considered here exhibit a local generation group SU(2)G × U(1)G. For the solutions with broken SO(10) symmetry, the leptons and quarks within one generation transform differently with respect to SU(2)G × U(1)G. Spontaneous symmetry breaking also modifies the SO(10) relations among Yukawa couplings. All this has important consequences for possible fermion mass relations obtained from higher-dimensional theories.

We argue that the vamshmg of the cosmological constant obtains as a result of the dynamics of a new field-the cosmon-which is the Goldstone boson of dilatation lnvanance, assumed to be broken spontaneously near the Planck scale The presence of the cosmon, coupled to the fact that scale lnvarlance is anomalous at the quantum level, drives the cosmological constant to zero, provided that the energy-momentum trace is purely anomalous. Furthermore, these quantum anomalies give the cosmon a small mass, giving rise to an intermediate range force (2~< 10 4 m). We can eshmate the effect of the cosmon force between macroscopic matter distributions The dominant component of the force is attractive, couples to mass and should be weaker than gravity (a ~ 10-2 10 3). There is, however, also a repulsive baryon-number-dependent component of calculable strength ( ~ ~a) and an even smaller contribution proportional to Z-N. Einstein's equations admit Minkowski space as a solution only if the trace of the energy-momentum tensor T ~" in vacuum vanishes (( T~ ) is the cosmological constant). In the standard model of the strong and electroweak interactions, however, there exist various nonvanishing contributions to this trace. For instance, chiral symmetry breaking in QCD gives a contribution to (Ta a) proportional to (mulaU 2

We discuss cosmologies where the Planck length is not a fundamental constant but rather evolves with time. The dynamics which should be responsible for today's tiny value of this length scale are governed by the effective potential of a Brans-Dicke type theory. Qualitative properties of this potential depend on the short distance behaviour of the unifying fundamental theory. We discuss criteria for the asymptotic behaviour of realistic cosmologies and show that the role of a possible cosmological constant is quite different from the case of standard cosmology.

Gravity in 13 dimensions with ground state M 4 × S 9 exhibits a local SO(10) gauge group. We discuss the dimensional reduction for this model. The model is enlarged to 17 dimensions to include a generation group for four fermion generations.

Some consequences of an SO(10) gauge theory which breaks down to SU(3)c × U(1)e.m. via SU(4)c × SU(2)L × SU(2)R are presented. These include: (i) A proton lifetime estimate of (1–20) × 1031 yr. (ii) Mass relations involving quarks and charged leptons. The explanation of the violation of the asymptotic SU(5) relation me = md is linked to the new intermediate mass scale in SO(10). The top quark mass is estimated to be 20 ± 2 GeV at the toponium mass. (iii) The possibility of a fourth generation (ντ′, τ′, b′, t′) with mτ′ ≅ 17–35 GeV, m b ′ ⋍ 42–118 GeV and m t ′ ⋍ 150–230 GeV . (iv) Heaviest neutrino mass in the 1–10 eV range. In addition, the masses of the superheavy neutrinos are of order 5 × 1012 − 5 × 1013 GeV. (v) Neutron-antineutron oscillations with τ n n > 10 38 yr.

Higher dimensional theories predict ratios between Yukawa couplings and gauge couplings in the resulting four-dimensional gauge theory. After spontaneous symmetry breaking of weak interactions, these relations are converted into relations between particle masses. We calculate explicitly the Yukawa couplings resulting from a six-dimensional SO(12) gauge theory. We argue that the fermion masses follow the pattern mt, ≫ mb, mc mτ ≫ ms, mμ ≫ md, mu, me.

We consider fermions in theories of higher dimensional gravity where the four-dimensional gauge group is embedded in the invariance group of d dimensional (d>4) Lorentz and general co-ordinate transformations. It is a necessary condition for obtaining massless chiral fermions from dimensional reduction that the d dimensional spinor does not admit a mass term consistent with Lorentz and general co-ordinate transformations. This is the case for a Weyl spinor for d = 6 8 mod 8, a Majorana spinor for d = 9 mod 8 or a Majorana-Weyl spinor for d = 2 mod 8.

Models are considered which have no small Yukawa couplings unrelated to symmetry. This situation is generic in higher dimensional unification where Yukawa couplings are predicted to have a strength similar to the gauge couplings. Generations have then to be differentiated by symmetry properties and the structure of fermion mass matrices is given in terms of quantum numbers alone. Possible symmetries leading to realistic mass matrices are scanned.

Certain embeddings of the low energy SU(3) C × SU(2) L × U(1) Y gauge group within the higher dimensional symmetry lead to exotic chiral generations in addition to a number of standard generations. An example is studied, leading to an anomaly free chiral exotic generation consisting of quarks with electric charge + 1 6 and − 5 6 , the corresponding antiquarks and addition integer charged leptons. The most striking predictions from such a compactification would be the existence of stable half-integer charged hadrons with a mass of the order of the Fermi scale. Detection of such particles would be an impressive hint for the existence of more than four dimensions.

Within the context of a class of higher dimensional models of gravity, we investigate the heating of the universe following an inflationary phase. High temperatures, typically on the order of 10 17 GeV can be achieved. This allows for a subsequent production of baryon asymmetry and, if existing, superheavy cosmic strings.