Feynman parametrization and Mellin summation at finite temperature

Journal Article · Sat Nov 01 04:00:00 EDT 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.78.096001· OSTI ID:21254646

Ayala, Alejandro ^[1]; Piccinelli, Gabriella ^[2]; Sanchez, Angel ^[3]; Tejeda-Yeomans, Maria Elena ^[4]

---

1. Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, Mexico Distrito Federal 04510 (Mexico)
2. Centro Tecnologico, FES Aragon, Universidad Nacional Autonoma de Mexico, Avenida Rancho Seco S/N, Bosques de Aragon, Nezahualcoyotl, Estado de Mexico 57130 (Mexico)
3. Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Apartado Postal 2-82, Morelia, Michoacan 58040 (Mexico)
4. Departameto de Fisica, Universidad de Sonora, Boulevard Luis Encinas J. y Rosales, Colonia Centro, Hermosillo, Sonora 83000 (Mexico)

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 end point 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.

• OSTI ID: 21254646
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 9 Vol. 78; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
FIELD THEORIES
MAGNETIC FIELDS
MELLIN TRANSFORM
PERIODICITY
SINGULARITY