Feynman parametrization and Mellin summation at finite temperature

Abstract

We show that the Mellin summation technique (MST) is a well defined and useful tool to compute loop integrals at finite temperature in the imaginary-time formulation of thermal field theory, especially when interested in the infrared limit of such integrals. The method makes use of the Feynman parametrization which has been claimed to have problems when the analytical continuation from discrete to arbitrary complex values of the Matsubara frequency is performed. We show that without the use of the MST, such problems are not intrinsic to the Feynman parametrization but instead, they arise as a result of (a) not implementing the periodicity brought about by the possible values taken by the discrete Matsubara frequencies before the analytical continuation is made and (b) to the changing of the original domain of the Feynman parameter integration, which seemingly simplifies the expression but in practice introduces a spurious endpoint singularity. Using the MST, there are no problems related to the implementation of the periodicity but instead, care has to be taken when the sum of denominators of the original amplitude vanishes. We apply the method to the computation of loop integrals appearing when the effects of external weak magnetic fields on the propagation of scalar particles is considered.

16 pages, 1 figure. Discussion expanded. References added. Published version

References in corpus (4)

• Effective potential at finite temperature in a constant magnetic field I: Ring diagrams in a scalar theory
• Effective potential at finite temperature in a constant hypermagnetic field: Ring diagrams in the Standard Model
• Derivative expansions of Euclidean thermal effective actions
• Uniqueness of the Thermal Effective Potential

Cited by in corpus (5)

• Inverse magnetic catalysis for the chiral transition induced by thermo-magnetic effects on the coupling constant
• Inverse magnetic catalysis in the linear sigma model with quarks
• Symmetry restoration at finite temperature with weak magnetic fields
• A note on the infrared behavior of the compactified Ginzburg--Landau model in a magnetic field
• On kinetic theories with color and spin from amplitudes