arXiv subjects

C. Wetterich

Publications and source records attributed to C. Wetterich.

At least 163 records · Page 9Linked to original sources

arXiv1998

Equation of state near the endpoint of the critical line

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.

cond-mat↗

arXiv1998

Time evolution of correlation functions for classical and quantum anharmonic oscillators

The time evolution of the correlation functions of an ensemble of anharmonic N-component oscillators with O(N) symmetry is described by a flow equation, exact up to corrections of order $1/N^2$. We find effective irreversibility. Nevertheless, analytical and numerical investigation reveals that the system does not reach thermal equilibrium for large times, even when $N\to \infty$. Depending on the initial distribution, the dynamics is asymptotically stable or it exhibits growing modes which break the conditions for the validity of the 1/N expansion for large time. We investigate both classical and quantum systems, the latter being the limit of an O(N) symmetric scalar quantum field theory in zero spatial dimensions.

hep-ph↗

arXiv1997

Nonperturbative Flow Equations, Low-Energy QCD and the Chiral Phase Transition

We review the formalism of the effective average action in quantum field 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 finally 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 $T_c$ turns out to be smaller than its zero temperature value.

hep-ph↗

arXiv1997

Gluon Condensation in Nonperturbative Flow Equations

We employ nonperturbative flow equations for an investigation of the effective action in Yang-Mills theories. We compute the effective action $Γ[B]$ for constant color magnetic fields $B$ and examine Savvidy's conjecture of an unstable perturbative vacuum. Our results indicate that the absolute minimum of $Γ[B]$ occurs for B=0. Gluon condensation is described by a nonvanishing expectation value of the regularized composite operator $F_{μν}F^{μν}$ which agrees with phenomenological estimates.

hep-th↗

arXiv1997

Two flavor chiral phase transition from nonperturbative flow equations

We employ nonperturbative flow equations to compute the equation of state for two flavor QCD within an effective quark meson model. This yields the temperature and quark mass dependence of quantities like the chiral condensate or the pion mass. 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 T_c turns out to be smaller than its zero temperature value.

hep-ph↗

arXiv1997

Effective Nonlocal Euclidean Gravity

A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newton's constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they may lead to a value $Ω<1$ for the critical density after inflation. The simplest model considered here appears to be in conflict with nucleosynthesis, but generalizations consistent with all cosmological observations seem conceivable.

gr-qc↗

arXiv1997

The Linear Meson Model and Chiral Perturbation Theory

We compare the linear meson model and chiral perturbation theory in next to leading order in the quark mass expansion. In particular, we compute the couplings L_4--L_8 of chiral perturbation theory as functions of the parameters of the linear model. They are induced by the exchange of 0^{++} scalar mesons. We use a phenomenological analysis of the effective vertices of the linear model in terms of pseudoscalar meson masses and decay constants. Our results for the L_i agree with previous phenomenological estimates.

hep-ph↗

arXiv1997

Non-Equilibrium Time Evolution in Quantum Field Theory

The time development of equal-time correlation functions in quantum mechanics and quantum field theory is described by an exact evolution equation for generating functionals. This permits a comparison between classical and quantum evolution in non-equilibrium systems.

hep-th↗

arXiv1996

Coarse graining and first order phase transitions

We discuss the dependence of the coarse grained free energy and the classical interface tension on the coarse graining scale $k$. A stable range appears only if the renormalized dimensionless couplings at the critical temperature are small. This gives a quantitative criterion for the validity of computations within Langer's theory of spontaneous bubble nucleation.

hep-ph↗

arXiv1996

Nonperturbative Flow Equations and Low--Energy QCD

hep-ph↗

arXiv1996

Equation of state and coarse grained free energy for matrix models

We investigate phase transitions in three dimensional scalar matrix models, with special emphasis on complex $2 \times 2$ matrices. The universal equation of state for weak first order phase transitions is computed. We also study the coarse grained free energy. Its dependence on the coarse graining scale gives a quantitative criterion for the validity of the standard treatment of bubble nucleation.

hep-th↗

arXiv1996

Quark masses from the linear meson model

Quark mass ratios are expressed within the linear meson model by universal relations involving only the masses and decay constants of the flavored pseudoscalars as well as their wave function renormalization. Quantitative results are in agreement with those obtained from chiral perturbation theory, with a tendency to a somewhat higher strange quark mass.

hep-ph↗

arXiv1996

Effective linear meson model

The effective action of the linear meson model generates the mesonic n-point functions with all quantum effects included. Based on chiral symmetry and a systematic quark mass expansion we derive relations between meson masses and decay constants. The model ``predicts'' values for f_eta and f_eta' which are compatible with observation. This involves a large momentum dependent eta-eta' mixing angle which is different for the on--shell decays of the eta and the eta'. We also present relations for the masses of the 0^{++} octet. The parameters of the linear meson model are computed and related to cubic and quartic couplings among pseudoscalar and scalar mesons. We also discuss extensions for vector and axialvector fields. In a good approximation the exchange of these fields is responsible for the important nonminimal kinetic terms and the eta-eta' mixing encountered in the linear meson model.

hep-ph↗

arXiv1996

Quantum Liouville Field Theory as Solution of a Flow Equation

A general framework for the Weyl invariant quantization of Liouville field theory by means of an exact renormalization group equation is proposed. This flow equation describes the scale dependence of the effective average action which has a built-in infrared cutoff. For c<1 it is solved approximately by a truncation of the space of action functionals. We derive the Ward identities associated to Weyl transformations in presence of the infrared cutoff. They are used to select a specific universality class for the renormalization group trajectory which is found to connect two conformal field theories with central charges 25-c and 26-c, respectively.

hep-th↗

arXiv1996

Effective quark interactions from QCD

We propose a new method for an analytical, non-perturbative computation of effective quark interactions from QCD. It is based on an exact flow equation which describes the scale dependence of the effective average action for quarks in presence of gluons.

hep-th↗

arXiv1996

Flow of the Coarse Grained Free Energy for Crossover Phenomena

The critical behaviour of a system of two coupled scalar fields in three dimensions is studied within the formalism of the effective average action. The fixed points of the system are identified and the crossover between them is described in detail. Besides the universal critical behaviour, the flow of the coarse grained free energy also describes the approach to scaling.

cond-mat↗

arXiv1996

The Ward Identity from the Background Field Dependence of the Effective Action

The dependence of the effective action for gauge theories on the background field obeys an exact identity. We argue that for Abelian theories the Ward identity follows from the more general background field identity. This observation is particularly relevant for the anomalous Ward identity valid for gauge theories with an effective infrared cutoff as used for flow equations.

hep-th↗

arXiv1995

Phase Diagram of Superconductors from Non-Perturbative Flow Equations

The universal behaviour of superconductors near the phase transition is described by the three-dimensional field theory of scalar quantum electrodynamics. We approximately solve the model with the help of non-perturbative flow equations. A first- or second-order phase transition is found depending on the relative strength of the scalar versus the gauge coupling. The region of a second-order phase transition is governed by a fixed point of the flow equations with associated critical exponents. We also give an approximate description of the tricritical behaviour and briefly discuss the crossover relevant for the onset of scaling near the critical temperature. Final confirmation of a second-order transition for strong type-II superconductors requires further analysis with extended truncations of the flow equations.

hep-ph↗