Gaussian Wavefunctional Approach in Thermofield Dynamics

TL;DR

This paper develops a Gaussian wavefunctional approach within thermofield dynamics to analyze finite temperature effects in scalar quantum field theories, providing a new method to compute thermal potentials and excited states.

Contribution

It introduces a Gaussian wavefunctional framework in thermofield dynamics, enabling calculation of thermal potentials and excited states for scalar fields with arbitrary potentials.

Findings

Finite temperature Gaussian effective potential derived.

Thermo-particle energies computed at finite temperature.

Results recover zero-temperature quantum field theory limits.

Abstract

The Gaussian wavefunctional approach is developed in thermofield dynamics. We manufacture thermal vacuum wavefunctional, its creation as well as annihilation operators,and accordingly thermo-particle excited states. For a (D+1)-dimensional scalar field system with an arbitrary potential whose Fourier representation exists in a sense of tempered distributions, we calculate the finite temperature Gaussian effective potential (FTGEP), one- and two-thermo-particle-state energies. The zero-temperature limit of each of them is just the corresponding result in quantum field theory, and the FTGEP can lead to the same one of each of some concrete models as calculated by the imaginary time Green function.