The Barton Expansion and the Path Integral Approach in Thermal Field Theory

TL;DR

This paper demonstrates the equivalence of the Barton expansion and the quantum mechanical path integral in thermal field theory and applies the QMPI to compute high-temperature effects in QED, confirming previous results.

Contribution

It establishes the equivalence between two methods for thermal field theory calculations and applies QMPI to derive high-temperature expansions in QED.

Findings

Confirmed the equivalence of Barton expansion and QMPI methods.

Computed high-temperature expansion for QED four-point function.

Results align with previous Barton expansion calculations.

Abstract

It has been shown how on-shell forward scattering amplitudes (the ``Barton expansion'') and quantum mechanical path integral (QMPI) can both be used to compute temperature dependent effects in thermal field theory. We demonstrate the equivalence of these two approaches and then apply the QMPI to compute the high temperature expansion for the four-point function in QED, obtaining results consistent with those previously obtained from the Barton expansion.