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 non-zero 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.

13 pages, 4 figures. Revised version (minor changes) accepted for publication in Phys. Rev. D

References in corpus (8)

• Renormalization Group Theory of the Three-Dimensional Dilute Bose Gas
• Multiple Scattering Expansion of the Self-Energy at Finite Temperature
• Finite Temperature Perturbation Theory and Large Gauge Invariance
• Out of Equilibrium Phase Transitions and a Toy Model for Disoriented Chiral Condensates
• Isolating vacuum amplitudes in quantum field calculations at finite temperature
• Thermal Operator Representation of Finite Temperature Graphs
• The thermal operator representation for Matsubara sums
• An operator representation for Matsubara sums

Cited by in corpus (13)

• Finite Temperature Effective Actions
• Quantum mass correction for the twisted kink
• Factorization of finite temperature graphs in thermal QED
• Effective actions at finite temperature
• Hard thermal effective actions in the Schwinger formulation
• Forward scattering amplitudes and the thermal operator representation
• Exact Effective action for (1+1)-dimensional fermions in an Abelian background at finite temperature and chemical potential
• Thermal Operator and Cutting Rules at Finite Temperature and Chemical Potential
• Thermal effective action for 1+1 dimensional massive QED
• Bogoliubov transformation and the thermal operator representation in the real time formalism
• Real-time thermal photon-photon interactions in the mixed space
• Hard thermal effective action in QCD through the thermal operator
• Thermal Operator and Dispersion Relation in QED at Finite Temperature and Chemical Potential