Applications of the Mellin-Barnes integral representation

TL;DR

This paper explores the use of Mellin-Barnes integral representation to derive asymptotic expansions relevant to mathematical physics, including zeta-functions, partition functions, and applications in quantum field theory and string theory.

Contribution

It introduces new asymptotic expansion techniques using Mellin-Barnes integrals for various functions in mathematical physics, enhancing analytical tools in the field.

Findings

Derived asymptotic expansions of zeta-functions and partition functions.

Applied results to high-temperature quantum field theory in curved spacetime.

Analyzed asymptotics of determinants in string theory.

Abstract

We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions. These results are then employed in different topics of quantum field theory, which include the high-temperature expansion of the free energy of a scalar field in ultrastatic curved spacetime, the asymptotics of the $p$-brane density of states, and an explicit approach to the asymptotics of the determinants that appear in string theory.