Applications of the Mellin-Barnes integral representation. (English) Zbl 1071.33501
Summary: 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 in 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.
MSC:
33C90 | Applications of hypergeometric functions |
81T20 | Quantum field theory on curved space or space-time backgrounds |
81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |