Applications of the Mellin-Barnes integral representation

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.

20 pages, LaTex

References in corpus (2)

• The Vacuum Energy Density for Spherical and Cylindrical Universes
• Possible Evidences of Kaluza-Klein Particles in a Scalar Model with Spherical Compactification

Cited by in corpus (11)

• Heat-kernel coefficients of the Laplace operator on the D-dimensional ball
• Trace Anomaly in Quantum Spacetime Manifold
• Bose-Einstein condensation under external conditions
• Multiple Mellin-Barnes Integrals as Periods of Calabi-Yau Manifolds With Several Moduli
• Quantum Correction to the Entropy of the (2+1)-Dimensional Black Hole
• Microcanonical fluctuations of the condensate in weakly interacting Bose gases
• Casimir Energy and Brane Stability
• Topological symmetry breaking of self--interacting fractional Klein--Gordon field on toroidal spacetime
• Bose-Einstein Condensation on Product Manifolds
• On the Hurwitz Zeta Function of Imaginary Second Argument
• Lamb shift of non-degenerate energy level systems placed between two infinite parallel conducting plates