# 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 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, 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.

- Authors:

- Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil)
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627-0171 (United States)
- Departamento de Fisica, Universidad Tecnica Federico Santa Maria, Casilla 110-V, Valparaiso (Chile)
- Departamento de Fisica, Universidade Federal do Para, Belem, Para 66075-110 (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; SELF-ENERGY; 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 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, 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.},

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}

}