Finite Temperature Effective Action Research Articles

Effective action for cosmological scalar fields at finite temperature

Scalar fields appear in many theories beyond the Standard Model of particle physics. In the early universe, they are exposed to extreme conditions, including high temperature and rapid cosmic expansion. Understanding their behavior in this environment is crucial to understand the implications for cosmology. We calculate the finite temperature effective action for the field expectation value in two particularly important cases, for damped oscillations near the ground state and for scalar fields with a flat potential. We find that the behavior in both cases can in good approximation be described by a complex valued effective potential that yields Markovian equations of motion. Near the potential minimum, we recover the solution to the well-known Langevin equation. For large field values we find a very different behavior, and our result for the damping coefficient differs from the expressions frequently used in the literature. We illustrate our results in a simple scalar model, for which we give analytic approximations for the effective potential and damping coefficient. We also provide various expressions for loop integrals at finite temperature that are useful for future calculations in other models.

Langevin description of gauged scalar fields in a thermal bath

We study the dynamics of the oscillating gauged scalar field in a thermal bath. A Langevin type equation of motion of the scalar field, which contains both dissipation and fluctuation terms, is derived by using the real-time finite temperature effective action approach. The existence of the quantum fluctuation-dissipation relation between the non-local dissipation term and the Gaussian stochastic noise terms is verified. We find the noise variables are anti-correlated at equal-time. The dissipation rate for the each mode is also studied, which turns out to depend on the wavenumber.

Chiral modulations in curved space II: conifold geometries

In this paper, we extend our previous analysis concerning the formation of inhomogeneous condensates in strongly-coupled fermion effective field theories on curved spaces and include the case of conifold geometries that represent the simplest tractable case of manifolds with curvature singularities. In the set-up considered here, by keeping the genuine thermodynamical temperature constant, we may single out the role that curvature effects play on the breaking/restoration of chiral symmetry and on the appearance of inhomogeneous phases. The first goal of this paper is to construct a general expression of the finite temperature effective action for inhomogeneous condensates in the case of four-fermion effective field theories on conifold geometries with generic Riemannian smooth base (generalised cones). The other goal is to implement numerically the above formal results and construct self-consistent solutions for the condensate. We explicitly show that the condensate assumes a kink-like profile, vanishing at the singularity that is surrounded by a bubble of restored chiral symmetry phase.

Finite temperature effective actions

In this lecture we will describe a systematic method for evaluating effective actions at finite temperature. The method will be illustrated with the effective actions for the 0 + 1 dimensional massive QED as well as for the 1 + 1 dimensional QED with massless or massive fermions.

Thermal effective action for1+1dimensional massive QED

In continuation of our earlier proposal for evaluating thermal effective actions, we determine the exact fermion propagator in 1+1 dimensional massive QED. This propagator is used to derive the finite temperature effective action of the theory which generates systematically all the one loop Feynman amplitudes calculated in thermal perturbation theory. Various aspects of the effective action including its imaginary part are discussed.

Nonperturbative QED effective action at finite temperature

We propose a novel method for the effective action of spinor and scalar QED at finite temperature in time-dependent electric fields, where charged pairs evolve in a nonadiabatic way. The imaginary part of the effective action consists of thermal loops of the Fermi-Dirac or Bose-Einstein distribution for the initial thermal ensemble, weighted with factors of the Bogoliubov coefficients for quantum effects. And the real part of the effective action is determined by the mean number of produced pairs and vacuum polarization at zero temperature. In the weak-field limit, the mean number of produced pairs is shown twice the imaginary part. We explicitly find the finite-temperature effective action in a constant electric field.

Effective actions at finite temperature

This is a more detailed version of our recent paper where we proposed, from first principles, a direct method for evaluating the exact fermion propagator in the presence of a general background field at finite temperature. This can, in turn, be used to determine the finite temperature effective action for the system. As applications, we discuss the complete one loop finite temperature effective actions for $0+1$ dimensional QED as well as for the Schwinger model in detail. These effective actions, which are derived in the real time (closed time path) formalism, generate systematically all the Feynman amplitudes calculated in thermal perturbation theory and also show that the retarded (advanced) amplitudes vanish in these theories. Various other aspects of the problem are also discussed in detail.

Finite temperature effective actions

We present, from first principles, a direct method for evaluating the exact fermion propagator in the presence of a general background field at finite temperature, which can be used to determine the finite temperature effective action for the system. As applications, we determine the complete one loop finite temperature effective actions for (0+1)-dimensional QED as well as the Schwinger model. These effective actions, which are derived in the real time (closed time path) formalism, generate systematically all the Feynman amplitudes calculated in thermal perturbation theory and also show that the retarded (advanced) amplitudes vanish in these theories.

Large gauge invariance in non-Abelian finite temperature effective actions

We analyze large gauge invariance in the non-Abelian, finite temperature context and its physical consequences for D = 3 effective actions. After briefly reviewing the structure of bundles and large gauge transformations that arise in nonsimply connected 3-manifolds and gauge groups, we discuss their connections to Chern-Simons terms and Wilson-Polyakov loops. We then provide an invariant characterization of the “Abelian” fluxes encountered in explicit computations of finite temperature effective actions. In particular we relate, and provide explicit realizations of, these fluxes to a topological index that measures the obstruction to global diagonalization of the loops around compactified time. We also explore the fate of, and exhibit some everywhere smooth, large transformations for nonvanishing index in various topologies.

Finite temperature effective action in monopole background

We compute the CP-odd part of the finite temperature effective action for massive Dirac fermions in the presence of a Dirac monopole. We confirm that the induced charge is temperature dependent, and in the effective action we find an infinite series of CP-violating terms that generalize the familiar zero temperature F F ̃ term. These results are analogous to recent results concerning finite temperature induced Chern–Simons terms.

Finite temperature perturbation theory and large gauge invariance

We examine finite temperature perturbation theory for Chern-Simons theories, in the context of an analogue 0+1-dimensional model. In particular, we show how nonextensive terms arise in the perturbative finite temperature effective action, using both the real-time and imaginary-time formalisms. We illustrate how large gauge invariance is restored at all orders, despite being broken at any given order in perturbation theory. We discuss which aspects generalize to a perturbative analysis of finite temperature Chern-Simons terms in higher dimensions.

Chern-Simons topological term at finite temperature

The parity-violating topological term in the effective action for 2+1 massive fermions is computed at finite temperature in the presence of a constant background field strength tensor. Gauge invariance of the finite-temperature effective action is also discussed.

Finite Temperature Chern-Simons Coefficient

We compute the exact finite temperature effective action in a 0+1-dimensional field theory containing a topological Chern-Simons term, which has many features in common with 2+1-dimensional Chern-Simons theories. This exact result explains the origin and meaning of puzzling temperature dependent coefficients found in various naive perturbative computations in the higher dimensional models.

Gauge invariance and finite temperature effective actions of Chern-Simons gauge theories with fermions

We discuss the behavior of theories of fermions coupled to Chern-Simons gauge fields with a non-abelian gauge group in three dimensions and at finite temperature. Using non-perturbative arguments and gauge invariance, and in contradiction with perturbative results, we show that the coefficient of the Chern-Simons term of the effective actions for the gauge fields at finite temperature can be at most an integer function of the temperature. This is in a sense a generalized no-renormalization theorem. We also discuss the case of abelian theories and give indications that a similar condition should hold there too. We discuss consequences of our results to the thermodynamics of anyon superfluids and fractional quantum Hall systems.

Finite-temperature effective action and thermalization of perturbations

The effective action is computed for the λΦ 4-theory at finite temperature for small perturbations about a constant background field, using a generalized tadpole method. We find the complete effective action, including the real and imaginary parts, to all orders in derivatives and to order O( λ 2). The solutions of the dispersion relations show that initial perturbations do not necessarily thermalize fast enough to be absent at the onset of phase transition.

Radiatively induced first-order phase transitions the necessity of the renormalization group

We advocate a (Wilson) renormalization-group (RG) treatment of finite-temperature first-order phase transitions, in particular those driven by radiative corrections such as occur in the standard model, and other spontaneously broken gauge theories. We introduce the scale-dependent coarse-grained free energy S Λ [ φ] which we explicitly calculate, using the Wilson RG and a (4 − ε)-expansion, for a scalar toy model that shares many features of the gauged case. As argued by Langer and others, the dynamics of the phase transition are described by S Λ [ φ] with 1/Λ of order the bubble wall thickness, and not by the usual (RG-improved) finite-temperature effective action which is reproduced by S Λ [ φ] for Λ → 0. We argue that for weakly first-order transitions (such as that in the he (4 − ε)-expansion is necessary to control an inevitable growth of the effective scale-dependent coupling towards the strong-coupling regime, and that diagrammatic resummation techniques are unlikely to be appropriate.

Theory of density fluctuations in the O(4)-model of the QCD phase transition

Density fluctuations in small phase space bins for centrally produced particles are conveniently parametrized by a Gaussian free energy functional of the density fluctuation field. This observation leads to the investigation of the O( N) linear σ-model; the O(4) version serves as a prototype theory of the QCD chiral order parameter. We derive an exact, non-perturbative and finite equation for its finite temperature effective action. In the large- N limit, well-known results on the nature of the phase transition are recovered. Thus, we obtain the Ginzburg-Landau theory for a QCD system in thermodynamic equilibrium.

Thermalization of the Higgs field at the electroweak phase transition

The thermalization rate for long wavelength fluctuations in the Higgs field is calculated from the imaginary part of the finite temperature effective action in the unbroken phase of the Standard Model. We use improved propagators including a resummation of hard thermal loops. The thermalization rate is computed at one-loop level, but an estimate of the two-loop contribution appears to give an indication that they are comparable to the one-loop result for small thermal Higgs mass. We show also that the Higgs field fluctuations are likely to thermalize very fast compared with the electroweak phase transition time.

Corrections to the electroweak effective action at finite temperature.

We calculate contributions to the finite temperature effective action for the electroweak phase transition (EWPT) at $O({g}^{4})$, i.e., at second order in ($\frac{{g}^{2}T}{\mathcal{M}}$) and all orders in ($\frac{{g}^{2}{T}^{2}}{{\mathcal{M}}^{2}}$). This requires plasma-mass corrections in the calculation of the effective potential, the inclusion of the "lollipop" diagram, and an estimate of derivative corrections. We find the EWPT remains too weakly first order to drive baryogenesis. We calculate some one-loop kinetic energy corrections using both functional and diagrammatic methods; these may be important for saddle point configurations such as the bounce or sphaleron.

Erratum: Mass gap of the nonlinear- sigma model through the finite-temperature effective action

Erratum: Mass gap of the nonlinear- sigma model through the finite-temperature effective action