Thermal operator representation of feynman graphs

Abstract

In this talk I describe an interesting relation between Feynman graphs at finite temperature and chemical potential and the corresponding ones at zero temperature. The operator relating the two which we call the "thermal operator", simplifies the evaluation of finite temperature graphs and helps in understanding better several physical questions such as cutting rules, forward scattering, gauge invariance etc at finite temperature.

Local and Nonlocal Thermal Field Theory

“…One is free to choose any value between 0 and 1 for the real parameter σ, but two choices have proven to be specifically fruitful. For σ = 1, one obtains the Keldysh-Schwinger (or closed time path) formalism which can used to describe non-equilibrium phenomena [1]. For σ = 1/2, the real time formalism corresponds to thermofield dynamics of Umezawa et.…”

“…The unphysical parameter σ never appears in the final results. Figures were taken from [1] 27 2.2 Frequency sums can be expressed as complex contour integrals because β 2 coth βp 0 /2 produces a collection of poles with unit residue at p 0 = iω n . A subsequent contour deformation allows one to employ either contour C 2 or C 3 , both of which cover the entire complex plane except the imaginary axis and differ in the sign of the residues only.…”

“…[L] = E 4 . 1 Additionally, it is important to realize that the often recurring terms [T ] = [M ] = E, where T is temperature and M the so-called scale of nonlocality (the meaning of which will be discussed in length in chapter 1).…”

“…4 Thermal field theory allows one to study phase transitions involving symmetry restoration in the context of theories with a spontaneously broken symmetry such as the electroweak theory. Questions such as 3 Calculations prove a lot more challenging than their zero temperature counterparts and there is "a continuous effort to simplify such calculations in order for thermal field theories to be embraced by the community at large" [1]. 4 From a philosophical point of view, thermal field theories (TFTs) ought to be more accurate theories than ordinary quantum field theories (QFTs).…”

“…Newton himself however already realized that one aspects of his theory could not be philosophically justified and recognized the severe problems entailed by this -gravitational effects from system A are instanteneously transferred onto another system, B, without these bodies being in physical contact. 1 Though sufficiently accurate for describing gravity on Earth, this nonlocal effect renders Newtonian mechanics useless in order to describe the grand structures in the universe, heavy objects such as neutron stars and, in general, situations in which relativistic effects should be taken into account. The successive well-entrenched theory of gravitation -Einstein's theory of General Relativity (GR) -eliminated this instantaneous action at a distance.…”