Search

We investigate the abundance of large-scale hot and cold spots in the WMAP-5 temperature maps and find considerable discrepancies compared to Gaussian simulations based on the LCDM best-fit model. Too few spots are present in the reliably observed cosmic microwave background (CMB) region, i.e., outside the foreground-contaminated parts excluded by the KQ75 mask. Even simulated maps created from the original WMAP-5 estimated multipoles contain more spots than visible in the measured CMB maps. A strong suppression of the lowest multipoles would lead to better agreement. The lack of spots is reflected in a low mean temperature fluctuation on scales of several degrees (4 to 8), which is only shared by less than 1% (0.16%-0.62%) of Gaussian LCDM simulations. After removing the quadrupole, the probabilities change to 2.5%-8.0%. This shows the importance of the anomalously low quadrupole for the statistical significance of the missing spots. We also analyze a possible violation of Gaussianity or statistical isotropy (spots are distributed differently outside and inside the masked region)., Comment: 12 pages; changes in the abstract, extended discussion of the quadrupole and the significances, minor clarifications, one added figure (behavior of typical simulations), one added reference

A quintessence scalar field or cosmon interacting with neutrinos can have important effects on cosmological structure formation. Within growing neutrino models the coupling becomes effective only in recent times, when neutrinos become non-relativistic, stopping the evolution of the cosmon. This can explain why dark energy dominates the universe only in a rather recent epoch by relating the present dark energy density to the small mass of neutrinos. Such models predict the presence of stable neutrino lumps at supercluster scales (~200 Mpc and bigger), caused by an attractive force between neutrinos which is stronger than gravity and mediated by the cosmon. We present a method to follow the initial non-linear formation of neutrino lumps in physical space, by integrating numerically on a 3D grid non-linear evolution equations, until virialization naturally occurs. As a first application, we show results for cosmologies with final large neutrino average mass ~2 eV: in this case, neutrino lumps indeed form and mimic very large cold dark matter structures, with a typical gravitational potential 10^{-5} for a lump size ~10 Mpc, and reaching larger values for lumps of about 200 Mpc. A rough estimate of the cosmological gravitational potential at small k in the non-linear regime, Phi_nu = 10^{-6} (k/k_0)^{-2}, 1.2x10^{-2} h/Mpc < k_0 < 7.8x10^{-2} h/Mpc, turns out to be many orders of magnitude smaller than an extrapolation of the linear evolution of density fluctuations. The size of the neutrino-induced gravitational potential could modify the spectrum of CMB anisotropies for small angular momenta., 17 pages, 16 figures, accepted for publication in Physical Review D, minor changes and corrections

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.

We formulate an effective action Γ k for averages of fields taken within a volume of size k −d. In contrast to the block-spin approach on the lattice we work in continuous (euclidean) space, preserving all symmetries. We establish how expectation values of operators with momenta smaller than k can be computed from Γ k. The average action at different scales is related by an exact renormalization group equation. We apply these ideas to the N-component φ 4 theory in the spontaneously broken phase and derive the one-loop renormalization group equations for the average potential. The average potential becomes convex as k → 0.

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.

We investigate the fermions of the standard model without a Higgs scalar. Instead, we consider a non-local four-quark interaction in the tensor channel which is characterized by a single dimensionless coupling $f$. Quantization leads to a consistent perturbative expansion for small $f$. The running of $f$ is asymptotically free and therefore induces a non-perturbative scale $\Lambda_{ch}$, in analogy to the strong interactions. We argue that spontaneous electroweak symmetry breaking is triggered at a scale where $f$ grows large and find the top quark mass of the order of $\Lambda_{ch}$. We also present a first estimate of the effective Yukawa coupling of a composite Higgs scalar to the top quark, as well as the associated mass ratio between the top quark and the W boson., Comment: 24 pages

The effect of particle-hole fluctuations for the BCS-BEC crossover is investigated by use of functional renormalization. We compute the critical temperature for the whole range in the scattering length $a$. On the BCS side for small negative $a$ we recover the Gorkov approximation, while on the BEC side of small positive $a$ the particle-hole fluctuations play no important role, and we find a system of interacting bosons. In the unitarity limit of infinite scattering length our quantitative estimate yields $T_c/T_F=0.264$. We also investigate the crossover from broad to narrow Feshbach resonances -- for the later we obtain $T_c/T_F=0.204$ for $a^{-1}=0$. A key ingredient for our treatment is the computation of the momentum dependent four-fermion vertex and its bosonization in terms of an effective bound-state exchange., 11 pages, 6 figures. Reference added

A number of positive and null results on the time variation of fundamental constants have been reported. It is difficult to judge whether or not these claims are mutually consistent, since the observable quantities depend on several parameters, namely the coupling strengths and masses of particles. The evolution of these coupling-parameters over cosmological history is also a priori unknown. A direct comparison requires a relation between the couplings. We explore several distinct scenarios based on unification of gauge couplings, providing a representative (though not exhaustive) sample of such relations. For each scenario we obtain a characteristic time dependence and discuss whether a monotonic time evolution is allowed. For all scenarios, some contradictions between different observations appear. We show how a clear observational determination of non-zero variations would test the dominant mechanism of varying couplings within unified theories., Formatting changes and minor typos, equivalent to published version. 35 pages (11pt article format), 8 figures

Within the two-dimensional repulsive t-t'-Hubbard model, an attractive coupling in the d-wave pairing channel is induced by antiferromagnetic fluctuations. We investigate this coupling using functional renormalization group equations. The momentum dependent d-wave coupling can be bosonized by the use of scale dependent field transformations. We propose an effective coarse grained model for the Hubbard model which is based on the exchange of antiferromagnetic and d-wave collective bosons., 11 pages, 13 figures, equivalent to published version

We investigate singular geometries which can be associated with warped branes in arbitrary dimensions. If the brane tension is allowed to be variable, the extremum condition for the action requires additional constraints beyond the solution of the field equations. In a higher dimensional world, such constraints arise from variations of the metric which are local in the usual four-dimensional spacetime, without changing the geometry of internal space. As a consequence, continuous families of singular solutions of the field equations, with arbitrary integration constants, are generically reduced to a discrete subset of extrema of the action, similar to regular spaces. As an example, no static extrema of the action with effective four-dimensional gravity exist for six-dimensional gravity with a cosmological constant. These findings explain why the field equations of the reduced four-dimensional theory are not consistent with arbitrary solutions of the higher dimensional field equations - consistency requires the additional constraints. The characteristic solutions for variable tension branes are non-static runaway solutions where the effective four-dimensional cosmological constant vanishes as time goes to infinity., Comment: 25 pages

We compare the sensitivity of a recent bound on time variation of the fine structure constant from optical clocks with bounds on time varying fundamental constants from atomic clocks sensitive to the electron-to-proton mass ratio, from radioactive decay rates in meteorites, and from the Oklo natural reactor. Tests of the Weak Equivalence Principle also lead to comparable bounds on present variations of constants. The "winner in sensitivity" depends on what relations exist between the variations of different couplings in the standard model of particle physics, which may arise from the unification of gauge interactions. WEP tests are currently the most sensitive within unified scenarios. A detection of time variation in atomic clocks would favour dynamical dark energy and put strong constraints on the dynamics of a cosmological scalar field., Comment: ~4 Phys Rev pages

We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For three dimensional dilute gases, we find an upper bound on the scattering length a which is of the order of the microphysical scale - typically the range of the Van der Waals interaction. In contrast to fermions near the unitary bound, no strong interactions occur for bosons with approximately pointlike interactions, thus explaining the high quantitative reliability of perturbation theory for most quantities. For zero temperature we compute the quantum phase diagram for bosonic quasiparticles with a general dispersion relation, corresponding to an inverse microphysical propagator with terms linear and quadratic in the frequency. We compute the temperature dependence of the condensate and particle density n, and find for the critical temperature T_c a deviation from the free theory, Delta T_c/T_c = 2.1 a n^{1/3}. For the sound velocity at zero temperature we find very good agreement with the Bogoliubov result, such that it may be used to determine the particle density accurately., Comment: 21 pages, 16 figures. Reference added

We discuss the naturalness of exponential potentials for quintessence, showing that the resulting almost flat direction in the space of scalar fields, as well as the small time dependent cosmon mass, can be related to an anomalous dilatation symmetry. We argue that the physics of the cosmological constant is Planck scale physics, and comment on the role of quantum fluctuations. We present three higher dimensional scenarios how a runaway of the ``cosmological constant'' to zero can be combined with stable particle physics properties, leading at most to small variations of the ``fundamental couplings''., Comment: 19 pages

Scalar field dynamics may give rise to a nonzero cosmological variation of fundamental constants. Within different scenarios based on the unification of gauge couplings, the various claimed observations and bounds may be combined in order to trace or restrict the time history of the couplings and masses. If the scalar field is responsible for a dynamical dark energy or quintessence, cosmological information becomes available for its time evolution. Combining this information with the time variation of couplings, one can determine the interaction strength between the scalar and atoms, which may be observed by tests of the Weak Equivalence Principle. We compute bounds on the present rate of coupling variation from experiments testing the differential accelerations for bodies with equal mass and different composition and compare the sensitivity of various methods. In particular, we discuss two specific models of scalar evolution: crossover quintessence and growing neutrino models., Comment: 26 pages, 2 figures; minor typos & added references, to be published in JCAP

We apply a field-theoretic functional renormalization group technique to the few-body (vacuum) physics of non-relativistic atoms near a Feshbach resonance. Three systems are considered: one-component bosons with U(1) symmetry, two-component fermions with U(1)\times SU(2) symmetry and three-component fermions with U(1) \times SU(3) symmetry. We focus on the scale invariant unitarity limit for infinite scattering length. The exact solution for the two-body sector is consistent with the unitary fixed point behavior for all considered systems. Nevertheless, the numerical three-body solution in the s-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3) fermions. The Efimov parameter for the one-component bosons and the three-component fermions is found to be approximately s=1.006, consistent with the result of Efimov., Comment: 21 pages, 6 figures, minor changes, published version

The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical interpretations to practical issues as quantum computing. In this note we demonstrate how quantum mechanics can emerge from classical statistical systems. We discuss conditions and circumstances for this to happen. Quantum systems describe isolated subsystems of classical statistical systems with infinitely many states. While infinitely many classical observables "measure" properties of the subsystem and its environment, the state of the subsystem can be characterized by the expectation values of only a few probabilistic observables. They define a density matrix, and all the usual laws of quantum mechanics follow. 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. 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., Comment: clearer distinction between system and quantum observables, new references, 13 pages

We investigate non-linear, spherically symmetric solutions to the coupled system of a quintessence field and Einstein gravity. In the presence of a scalar potential, we find regular solutions that to an outside observer very closely resemble Schwarzschild black holes. However, these cosmon lumps have neither a horizon nor a central singularity. A stability analysis reveals that our static solutions are dynamically unstable. It remains an open question whether analogous stable solutions exist., Comment: 6 pages, 5 figures

The energy spectrum for three species of identical fermionic atoms close to a Feshbach resonance is computed by use of a nonperturbative flow equation. Already a simple truncation shows that for large scattering length $|a|$ the lowest energy state is a "trion" (or trimer) bound state of three atoms. At the location of the resonance, for $|a|\to\infty$, we find an infinite set of trimer bound states, with exponentially decreasing binding energy. This feature was pointed out by Efimov. It arises from limit cycle scaling, which also leads to a periodic dependence of the three body scattering coupling on $\ln |a|$. Extending our findings by continuity to nonzero density and temperature we find that a "trion phase" separates a BEC and a BCS phase, with interesting quantum phase transitions for T=0., Comment: 9 pages, 4 figures, minor changes, reference added

We formulate an effective action for averages of fields for the coupled system of scalars and (chiral) fermions. The renormalization group equations for the scale dependence of the average potential exhibit a quadratic renormalization in addition to the usual logarithmic renormalization. It is independent of the regularization scheme and the momentum cutoff. We investigate to what extent quadratic relations for the top quark mass, which were formerly based on the vanishing of the quadratic divergence, can be motivated in the light of these results.

Big Bang nucleosynthesis (BBN) is the earliest sensitive probe of the values of many fundamental particle physics parameters. We have found the leading linear dependences of primordial abundances on all relevant parameters of the standard BBN code, including binding energies and nuclear reaction rates. This enables us to set limits on possible variations of fundamental parameters. We find that 7Li is expected to be significantly more sensitive than other species to many fundamental parameters, a result which also holds for variations of coupling strengths in grand unified (GUT) models. Our work also indicates which areas of nuclear theory need further development if the values of ``constants'' are to be more accurately probed., Refereed article to be published in Nuclear Physics in Astrophysics III Proceedings, J. Phys. G. Special Issue. Based on work in collaboration with C. Wetterich (Heidelberg). 6 pages

Functional renormalization yields a simple unified description of bosons at zero temperature, in arbitrary space dimension $d$ and for $M$ complex fields. We concentrate on nonrelativistic bosons and an action with a linear time derivative. The ordered phase can be associated with a nonzero density of (quasi) particles $n$. The behavior of observables and correlation functions in the ordered phase depends crucially on the momentum $k_{ph}$, which is characteristic for a given experiment. For the dilute regime $k_{ph}\gtrsim n^{1/d}$ the quantum phase transition is simple, with the same ``mean field'' critical exponents for all $d$ and $M$. On the other hand, the dense regime $k_{ph}\ll n^{1/d}$ reveals a rather rich spectrum of features, depending on $d$ and $M$. In this regime one observes for $d\leq 3$ a crossover to a relativistic action with second time derivatives. This admits order for $d>1$, whereas $d=1$ shows a behavior similar to the low temperature phase of the classical two-dimensional $O(2M)$-models., 31 pages, new references

The time evolution of a cosmological scalar field can be stopped by an increasing mass of the neutrinos. This leads to a transition from a cosmological scaling solution with dynamical dark energy at early time to a cosmological constant dominated universe at late time. The trigger for the transition is set at the time when the neutrinos become non-relativistic. The characteristic mass scale for dark energy is thus related to the neutrino mass, the only known particle physics scale in its vicinity. This explains the ``why now problem'' for dark energy. We present a particle physics realization of this ``growing matter'' scenario. It is based on the very slowly varying mass of a superheavy scalar triplet field whose expectation value dominates the light neutrino masses., Comment: new material on time varying constants, new figures, 8 pages, 4 figures

We analyze the effect of variation of fundamental couplings and mass scales on primordial nucleosynthesis in a systematic way. The first step establishes the response of primordial element abundances to the variation of a large number of nuclear physics parameters, including nuclear binding energies. We find a strong influence of the n‐p mass difference, of the nucleon mass and of A = 3,4,7 binding energies. A second step relates the nuclear parameters to the parameters of the Standard Model of particle physics. The deuterium, and, above all, 7Li abundances depend strongly on the average light quark mass. We calculate the behaviour of abundances when variations of fundamental parameters obey relations arising from grand unification. We also discuss the possibility of a substantial shift in the lithium abundance while the deuterium and 4He abundances are only weakly affected.

We analyze the effect of variation of fundamental couplings and mass scales on primordial nucleosynthesis in a systematic way. The first step establishes the response of primordial element abundances to the variation of a large number of nuclear physics parameters, including nuclear binding energies. We find a strong influence of the n-p mass difference (for the 4He abundance), of the nucleon mass (for deuterium) and of A=3,4,7 binding energies (for 3He, 6Li and 7Li). A second step relates the nuclear parameters to the parameters of the Standard Model of particle physics. The deuterium, and, above all, 7Li abundances depend strongly on the average light quark mass hat{m} \equiv (m_u+m_d)/2. We calculate the behaviour of abundances when variations of fundamental parameters obey relations arising from grand unification. We also discuss the possibility of a substantial shift in the lithium abundance while the deuterium and 4He abundances are only weakly affected., Comment: v2: 34 pages, 2 figures, typo in last GUT scenario corrected, added discussion and graph of nonlinear behaviour in GUT scenarios, added short section discussing binding of dineutron and 8Be, refs added, conclusions unaltered. Accepted for publication, Phys. Rev. D

A functional renormalisation group study for the BEC-BCS crossover for ultracold gases of fermionic atoms is presented. We discuss the fixed point which is at the origin of universality for broad Feshbach resonances. All macroscopic quantities depend only on one relevant parameter, the concentration a k_F, besides their dependence on the temperature in units of the Fermi energy. In particular, we compute the universal ratio between molecular and atomic scattering length in vacuum. We also present an estimate to which level of accuracy universality holds for gases of Li and K atoms., Comment: 19 pages, 3 figures, to be published in PRA

Antisymmetric tensor fields with chiral couplings to quarks and leptons may induce spontaneous electroweak symmetry breaking in a model without a ``fundamental'' Higgs scalar. No microscopic local mass term for the chiral tensors or ``chirons'' is allowed by the symmetries and our model exhibits only dimensionless couplings. However, the chiral couplings are asymptotically free and therefore generate a mass scale where they grow large. We argue that at this scale mass terms for the chiral tensor fields are generated non-perturbatively - the chirons appear as new massive spin one particles. Furthermore a scalar top-antitop condensate forms, giving mass to the weak gauge bosons and fermions. In this scenario the longstanding gauge hierarchy problem finds a solution similar to the mass generation in QCD. We compute the general form of the effective action for the chiral tensors and sketch several possibilities of their detection at LHC or through precision tests of the electroweak standard model., 30 pages, 7 figures

We investigate chiral symmetry breaking and color symmetry breaking in QCD. The effective potential of the corresponding scalar condensates is discussed in the presence of non-perturbative contributions from the semiclassical one-instanton sector. We concentrate on a color singlet scalar background which can describe chiral condensation, as well as a color octet scalar background which can generate mass for the gluons. Whereas a non-vanishing singlet chiral field is favored by the instantons, we have found no indication for a preference of color octet backgrounds., 25 pages, 7 figures

The first three years of observation of the Wilkinson Microwave Anisotropy Probe (WMAP) have provided the most precise data on the anisotropies of the cosmic microwave background (CMB) to date. We investigate the impact of these results and their combination with data from other astrophysical probes on cosmological models with a dynamical dark energy component. By considering a wide range of such models, we find that the constraints on dynamical dark energy are significantly improved compared to the first year data., Comment: 5 pages, 2 figures; v2: more explanatory title, added references, minor clarifications, matches published version

We review the formalism of the eective average action in quantum eld theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative approximations for its solution are discussed. This is applied to QCD where one observes the consecutive emergence of mesonic bound states and spontaneous chiral symmetry breaking as the coarse graining scale is lowered. We nally present a study of the chiral phase transition in two flavor QCD. A precision estimate of the universal critical equation of state for the three{dimensional O(4) Heisenberg model is presented. We explicitly connect the O(4) universal behavior near the critical temperature and zero quark mass with the physics at zero temperature and a realistic pion mass. For realistic quark masses the pion correlation length near Tc turns out to be smaller than its zero temperature value.

Chiral antisymmetric tensor fields can have chiral couplings to quarks and leptons. Their kinetic terms do not mix different representations of the Lorentz symmetry and a local mass term is forbidden by symmetry. The chiral couplings to the fermions are asymptotically free, opening interesting perspectives for a possible solution to the gauge hierarchy problem. We argue that the interacting theory for such fields can be consistently quantized, in contrast to the free theory which is plagued by unstable solutions. We suggest that at the scale where the chiral couplings grow large the electroweak symmetry is spontaneously broken and a mass term for the chiral tensors is generated non-perturbatively. Massive chiral tensors correspond to massive spin one particles that do not have problems of stability. We also propose an equivalent formulation in terms of gauge fields., additional material, concentrating on interactions with chiral fermions, 38 pages, 1 figure

We constrain the evolution of the dark energy density from Cosmic Microwave Background, Large Scale Structure and Supernovae Ia measurements. While Supernovae Ia are most sensitive to the equation of state $w_0$ of dark energy today, the Cosmic Microwave Background and Large Scale Structure data best constrains the dark energy evolution at earlier times. For the parametrization used in our models, we find $w_0 < -0.8$ and the dark energy fraction at very high redshift $��_{early} < 0.03$ at 95 per cent confidence level., 5 pages, 10 figures

We develop a functional integral formalism for ultracold gases of fermionic atoms. It describes the BEC - BCS crossover and involves both atom and molecule fields. Beyond mean field theory we include the fluctuations of the molecule field by the solution of gap equations. In the BEC limit, we find that the low temperature behavior is described by a Bogoliubov theory for bosons. For a narrow Feshbach resonance these bosons can be associated with microscopic molecules. In contrast, for a broad resonance the interaction between the atoms is approximately pointlike and microscopic molecules are irrelevant. The bosons represent now correlated atom pairs or composite ``dressed molecules''. The low temperature results agree with quantum Monte Carlo simulations. Our formalism can treat with general inhomogeneous situations in a trap. For not too strong inhomogeneities the detailed properties of the trap are not needed for the computation of the fluctuation effects - they enter only in the solutions of the field equations., Comment: 39 pages, 11 figures

Isotropization occurs on time scales much shorter than the thermal equilibration time. This is a crucial ingredient for the understanding of collision experiments of heavy nuclei or other nonequilibrium phenomena in complex many body systems. We discuss in detail the limitations of estimates based on standard ``linear'' or relaxation-time approximations, where isotropization and thermal equilibration rates agree. For a weak-coupling $\phi^4$-model the relaxation-time approximation underestimates the thermal equilibration time by orders of magnitude, in contrast to the isotropization time. The characteristic nonequilibrium isotropization rate can be enhanced as compared to the close-to-equilibrium value. Our results are obtained from the two-particle irreducible effective action, which includes off-shell and memory effects and does not involve a gradient expansion. This allows us to determine the range of validity of a description to lowest-order in gradients, which is typically employed in kinetic equations., Comment: 27 pages, 7 figures, NPB version, minor text changes

A six-dimensional universe with two branes in the "football-shaped" geometry leads to an almost realistic cosmology. We describe a family of exact solutions with time dependent characteristic size of internal space. After a short inflationary period the late cosmology is either of quintessence type or turns to a radiation dominated Friedmann universe where the cosmological constant appears as a free integration constant of the solution. The radiation dominated universe with relativistic fermions is analyzed in detail, including its dimensional reduction., Comment: 18 pages

The functional integral for QCD is reformulated by introducing explicitly an integration over the fluctuations of composite quark-antiquark bound states. Chiral symmetry breaking by the color singlet scalar field induces masses for the fermions. Our formulation with scalar fluctuations may be useful for lattice gauge theories by modifying the spectrum of the Dirac operator in the vacuum and permitting a simple connection to chiral perturbation theory. We propose that a ``condensate'' of quark-antiquark bound states in the color octet channel generates masses of the gluons by the Higgs mechanism. A simple effective action for quarks, gluons and (composite) scalars yields a surprisingly good description of the charges, masses and interactions of all low mass physical excitations - baryons, pseudoscalars and vector mesons. Dressed quarks appear as baryons and dressed gluons as vector mesons., 37 pages

We suggest a method for an approximative solution of the two dimensional Hubbard model close to half filling. It is based on partial bosonisation, supplemented by an investigation of the functional renormalisation group flow. The inclusion of both the fermionic and bosonic fluctuations leads in lowest order to agreement with the Hartree-Fock result or Schwinger-Dyson equation and cures the ambiguity of mean field theory . We compute the temperature dependence of the antiferromagnetic order parameter and the gap below the critical temperature. We argue that the Mermin-Wagner theorem is not practically applicable for the spontaneous breaking of the continuous spin symmetry in the antiferromagnetic state of the Hubbard model. The long distance behavior close to and below the critical temperature is governed by the renormalisation flow for the effective interactions of composite Goldstone bosons and deviates strongly from the Hartree-Fock result., New section on critical behavior 31 pages,17 figures

We suggest that the difference between time and space is due to spontaneous symmetry breaking. In a theory with spinors the signature of the metric is related to the signature of the Lorentz group. We discuss a higher symmetry that contains pseudo-orthogonal groups with an arbitrary signature as subgroups. The fundamental asymmetry between time and space can then result as a property of the ground state rather than being put into the formulation of the theory a priori. We show how the complex structure of quantum field theory as well as gravitational field equations arise from spinor gravity--a fundamental spinor theory without a metric.

We determine the influence of a variation of the fundamental ``constants'' on the predicted helium abundance in Big Bang Nucleosynthesis. The analytic estimate is performed in two parts: the first step determines the dependence of the helium abundance on the nuclear physics parameters, while the second step relates those parameters to the fundamental couplings of particle physics. This procedure can incorporate in a flexible way the time variation of several couplings within a grand unified theory while keeping the nuclear physics computation separate from any model-dependent assumptions., 8 pages, no figures

We investigate one-flavor QCD with an additional chiral scalar field. For a large domain in the space of coupling constants, this model belongs to the same universality class as QCD, and the effects of the scalar become unobservable. This is connected to a ``bound-state fixed point'' of the renormalization flow for which all memory of the microscopic scalar interactions is lost. The QCD domain includes a microscopic scalar potential with minima at nonzero field. On the other hand, for a scalar mass term m^2 below a critical value m_c^2, the universality class is characterized by perturbative spontaneous chiral symmetry breaking which renders the quarks massive. Our renormalization group analysis shows how this universality class is continuously connected with the QCD universality class., 33 pages, 6 figures, v2: presentation improved, results unchanged, version to appear in PRD

We propose a simple phenomenological parameterization of quintessence with a time-varying equation of state. In particular, it accounts for the possibility of early dark energy. The quintessence potential can be reconstructed in terms of the present fraction in dark energy, the present equation of state and the amount of early dark energy., Comment: 9 pages, LaTeX

Quantum correlations can be naturally formulated in a classical statistical system of infinitely many degrees of freedom. This realizes the underlying non-commutative structure in a classical statistical setting. We argue that the quantum correlations offer a more robust description with respect to the precise definition of observables.

We investigate the possibility of constructing a renormalizable standard model with purely fermionic matter content. The Higgs scalar is replaced by point-like fermionic self-interactions with couplings growing large at the Fermi scale. An analysis of the UV behavior in the point-like approximation reveals a variety of non-Gaussian fixed points for the fermion couplings. If real, such fixed points would imply nonperturbative renormalizability and evade triviality of the Higgs sector. For point-like fermionic self-interactions and weak gauge couplings, one encounters a hierarchy problem similar to the one for a fundamental Higgs scalar., 18 pages, 4 figures

We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of Einstein's equations due to the lack of local Lorentz-symmetry. We explore the generalized gravity with global instead of local Lorentz symmetry in first order of a systematic derivative expansion. At this level diffeomorphisms and global Lorentz symmetry allow for two new invariants in the gravitational effective action. The one which arises in the one loop approximation to spinor gravity is consistent with all present tests of general relativity and cosmology. This shows that local Lorentz symmetry is tested only very partially by present observations. In contrast, the second possible new coupling is severely restricted by present solar system observations., New material on absence of observational tests of local Lorentz invariance, 21 pages, to appear in Phys.Rev.D

We present a systematic treatment of the initial conditions and evolution of cosmological perturbations in a universe containing photons, baryons, neutrinos, cold dark matter, and a scalar quintessence field. By formulating the evolution in terms of a differential equation involving a matrix acting on a vector comprised of the perturbation variables, we can use the familiar language of eigenvalues and eigenvectors. As the largest eigenvalue of the evolution matrix is fourfold degenerate, it follows that there are four dominant modes with non-diverging gravitational potential at early times, corresponding to adiabatic, cold dark matter isocurvature, baryon isocurvature and neutrino isocurvature perturbations. We conclude that quintessence does not lead to an additional independent mode., Replaced with published version, 12 pages, 2 figures

The backreaction of structure formation influences the cosmological evolution equation for the homogenous and isotropic average metric. In a cold dark matter universe this effect leads only to small corrections unless a substantial fraction of matter is located in regions where strong gravitational fields evolve in time. A``cosmic virial theorem'' states that the sum of gravitational and matter pressure vanishes and therefore relates the average kinetic energy to a suitable average of the Newtonian potential. In presence of a scalar ``cosmon'' field mediating quintessence, however, cosmology could be modified if local cosmon fluctuations grow large. We speculate that this may trigger the accelerated expansion of the universe after the formation of structure., Comment: new "cosmic virial theorem",new references,LaTex,11 pages

The time variation of fundamental mass scales can have profound cosmological implications. We investigate a particular model of crossover quintessence which is compatible with all present cosmological observations. This model can also reconcile the reported time variation of the fine structure constant from quasar absorption lines with the bounds from archeo-nuclear physics and tests of the equivalence principle., 20 pages, LaTex

Crossover quintessence predicts that the time variation of fundamental couplings is substantially faster at redshift $z\approx 2$ than over the past few billion years. This could reconcile the reported time variation of the fine structure constant from quasar absorption lines with severe bounds from archeo-nuclear physics and high precision tests of the equivalence principle. We present a model that is consistent with all present data on time varying couplings, tests of the equivalence principle and cosmology., Comment: numerical example adapted to WMAP,published version,9 pages,LaTex

We compute the first order chiral phase transition for an instanton motivated quark model with a local six-quark interaction. In order to compare different solutions of the gap equation we compute the bosonic effective action -- a two particle irreducible free energy functional. We find that the first order transition ends for a critical current quark mass, with continuous crossover for larger quark masses. Furthermore, we investigate different possible order parameters, including a color octet condensate. We also compare our formalism with mean field theory., Comment: 10 pages, 3 figures, uses revtex4

A unified description of all interactions could be based on a higher-dimensional theory involving only spinor fields. The metric arises as a composite object and the gravitational field equations contain torsion-corrections as compared to Einstein gravity. Lorentz symmetry in spinor space is only global, implying new goldstone-boson-like gravitational particles beyond the graviton. However, the Schwarzschild and Friedman solutions are unaffected at one loop order. Our generalized gravity seems compatible with all present observations., Comment: 6 pages, LaTeX, v3: extended discussion and new references