Modified Laplace transformation method at finite temperature: application to infra-red problems of N component $\phi^4$ theory

TL;DR

This paper applies a modified Laplace transformation method to analyze finite temperature effects in N component ^4 theory, successfully extracting fractional power contributions in the massless limit at large N.

Contribution

It introduces a novel application of the modified Laplace transformation to finite temperature quantum field theory, enabling the calculation of fractional power terms in the massless limit.

Findings

Recovered fractional power contributions from truncated massive series.

Demonstrated the effectiveness of inverse Laplace transformation in evaluating fractional terms.

Re-examined the finite temperature problem in the large N limit of ^4 theory.

Abstract

Modified Laplace transformation method is applied to N component $\phi^4$ theory and the finite temperature problem in the massless limit is re-examined in the large N limit. We perform perturbation expansion of the dressed thermal mass in the massive case to several orders and try the massless approximation with the help of modified Laplace transformation. The contribution with fractional power of the coupling constant is recovered from the truncated massive series. The use of inverse Laplace transformation with respect to the mass square is crucial in evaluating the coefficients of fractional power terms.