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Title: Thermal operator representation of finite-temperature amplitudes in the presence of a chemical potential

Abstract

In a recent paper [Phys. Rev. D 72, 085006 (2005)], Brandt et al. deduced the thermal operator representation for a thermal N-point amplitude, both in the imaginary-time and real-time formalisms. In the case when a chemical potential present, however, the representation is not as simple as in the case with vanishing chemical potential. We propose a much simpler and transparent representation for the case of nonzero chemical potential.

Authors:
; ;  [1]
  1. Graduate School of Science, Osaka City University, Sumiyoshi-ku, Osaka 558-8585 (Japan)
Publication Date:
OSTI Identifier:
20776811
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.73.047702; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; CALCULATION METHODS; FIELD OPERATORS; POTENTIALS; QUANTUM FIELD THEORY

Citation Formats

Inui, M., Kohyama, H., and Niegawa, A. Thermal operator representation of finite-temperature amplitudes in the presence of a chemical potential. United States: N. p., 2006. Web. doi:10.1103/PhysRevD.73.047702.
Inui, M., Kohyama, H., & Niegawa, A. Thermal operator representation of finite-temperature amplitudes in the presence of a chemical potential. United States. doi:10.1103/PhysRevD.73.047702.
Inui, M., Kohyama, H., and Niegawa, A. Wed . "Thermal operator representation of finite-temperature amplitudes in the presence of a chemical potential". United States. doi:10.1103/PhysRevD.73.047702.
@article{osti_20776811,
title = {Thermal operator representation of finite-temperature amplitudes in the presence of a chemical potential},
author = {Inui, M. and Kohyama, H. and Niegawa, A.},
abstractNote = {In a recent paper [Phys. Rev. D 72, 085006 (2005)], Brandt et al. deduced the thermal operator representation for a thermal N-point amplitude, both in the imaginary-time and real-time formalisms. In the case when a chemical potential present, however, the representation is not as simple as in the case with vanishing chemical potential. We propose a much simpler and transparent representation for the case of nonzero chemical potential.},
doi = {10.1103/PhysRevD.73.047702},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 73,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}
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  • Combining the thermal operator representation with the dispersion relation in QED at finite temperature and chemical potential, we determine the complete retarded photon self-energy only from its absorptive part at zero temperature. As an application of this method, we show that, even for the case of a nonzero chemical potential, the temperature dependent part of the one loop retarded photon self-energy vanishes in (1+1) dimensional massless QED.
  • Using the mixed space representation (t,p{yields}) in the context of scalar field theories, we prove in a simple manner that the Feynman graphs at finite temperature are related to the corresponding zero temperature diagrams through a simple thermal operator, both in the imaginary time as well as in the real time formalisms. This result is generalized to the case when there is a nontrivial chemical potential present. Several interesting properties of the thermal operator are also discussed.
  • Using the mixed space representation, we extend our earlier analysis to the case of Dirac and gauge fields and show that in the absence of a chemical potential, the finite temperature Feynman diagrams can be related to the corresponding zero temperature graphs through a thermal operator. At nonzero chemical potential we show explicitly in the case of the fermion self-energy that such a factorization is violated because of the presence of a singular contact term. Such a temperature dependent term which arises only at finite density and has a quadratic mass singularity cannot be related, through a regular thermal operator,more » to the fermion self-energy at zero temperature which is infrared finite. Furthermore, we show that the thermal radiative corrections at finite density have a screening effect for the chemical potential leading to a finite renormalization of the potential.« less
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