Thermal operator representation of finite temperature graphs. II
Abstract
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 selfenergy 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, to the fermion selfenergy 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.
 Authors:
 Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil)
 Department of Physics and Astronomy, University of Rochester, Rochester, New York 146270171 (United States)
 Departamento de Fisica, Universidad Tecnica Federico Santa Maria, Casilla 110V, Valparaiso (Chile)
 Departamento de Fisica, Universidade Federal do Para, Belem, Para 66075110 (Brazil)
 Publication Date:
 OSTI Identifier:
 20782681
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.73.065010; (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; DENSITY; FACTORIZATION; FERMIONS; FEYNMAN DIAGRAM; GAUGE INVARIANCE; MASS; POTENTIALS; QUANTUM FIELD THEORY; RADIATIVE CORRECTIONS; RENORMALIZATION; SELFENERGY; SINGULARITY; TEMPERATURE DEPENDENCE
Citation Formats
Brandt, F.T., Frenkel, J., Das, Ashok, Espinosa, Olivier, and Perez, Silvana. Thermal operator representation of finite temperature graphs. II. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.065010.
Brandt, F.T., Frenkel, J., Das, Ashok, Espinosa, Olivier, & Perez, Silvana. Thermal operator representation of finite temperature graphs. II. United States. doi:10.1103/PHYSREVD.73.065010.
Brandt, F.T., Frenkel, J., Das, Ashok, Espinosa, Olivier, and Perez, Silvana. Wed .
"Thermal operator representation of finite temperature graphs. II". United States.
doi:10.1103/PHYSREVD.73.065010.
@article{osti_20782681,
title = {Thermal operator representation of finite temperature graphs. II},
author = {Brandt, F.T. and Frenkel, J. and Das, Ashok and Espinosa, Olivier and Perez, Silvana},
abstractNote = {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 selfenergy 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, to the fermion selfenergy 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.},
doi = {10.1103/PHYSREVD.73.065010},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}

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.

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