Thermal Field Theory in real-time formalism: concepts and applications for particle decays

This review represents a detailed and comprehensive discussion of the Thermal Field Theory (TFT) concepts and key results in Yukawa-type theories. We start with a general pedagogical introduction into the TFT in the imaginary- and real-time formulation. As phenomenologically relevant implications, we present a compendium of thermal decay rates for several typical reactions calculated within the framework of the real-time formalism and compared to the imaginary-time results found in the literature. Processes considered here are those of a neutral (pseudo)scalar decaying into two distinct (pseudo)scalars or into a fermion-antifermion pair. These processes are extended from earlier works to include chemical potentials and distinct species in the final state. In addition, a (pseudo)scalar emission off a fermion line is also discussed. These results demonstrate the importance of thermal effects in particle decay observables relevant in many phenomenological applications in systems at high temperatures and densities.

Quark mass function at finite density in real-time formalism

Chiral symmetry restoration of quarks is investigated at finite density in quantum chromodynamics. The critical chemical potentials at zero temperature, in which the chiral symmetry is restored, are calculated with the Schwinger-Dyson equation in the real-time formalism without the instantaneous exchange approximation. We present some properties of the quark mass functions and the quark propagators.

Thermal conductivity of hot pionic medium due to pion self-energy for πσ and πρ loops

The thermal conductivity of pionic medium has been evaluated with the help of its standard expression from the relaxation time approximation, where inverse of pion relaxation time or pion thermal width has been obtained from the imaginary part of pion self-energy. In the real-time formalism of thermal field theory, the finite temperature calculations of pion self-energy for πσ and πρ loops have been done. The numerical value of our thermal conductivity increases with temperature very softly, though at particular temperature, our estimation has to consider a large band of phenomenological uncertainty.

Activation instanton in real-time formalism

In this paper, we study the dynamics of the activation of a Brownian particle using the path integral formalism in real time. Along with the construction of the saddle-point (instanton) solutions, we develop the formalism allowing to calculate the effect of the fluctuations near this solution in detail. In particular, it is shown that there is a soft mode for which the integration is not Gaussian and just this mode is responsible for the finite probability flux.