Infrared nullification of the effective electromagnetic field at finite temperature

TL;DR

This paper investigates the infrared divergence problem of the effective electromagnetic field at finite temperature, demonstrating that the field effectively vanishes due to natural infrared regularization mechanisms.

Contribution

It introduces two regularization schemes showing that the effective electromagnetic field vanishes at finite temperature, providing a perturbative explanation for infrared nullification.

Findings

Effective field vanishes at finite temperature.

Infrared regularization via heat bath effects.

Perturbative proof of nullification of the electromagnetic field.

Abstract

The problem of infrared divergence of the effective electromagnetic field at finite temperature (T) is revisited. A model of single spatially localized electron interacting with thermal photons is considered in the limit T to 0 using two different regularization schemes. The first is based on the shift i 0 to i varepsilon of the electron propagator pole in the complex energy plane, and is used to explicitly calculate the effective field in the one-loop approximation. We show that the matrix-valued imaginary part of the electron self-energy can be consistently related to the pole shift, and that the presence of the heat bath leads to appearance of an effective varepsilon sim T, thus providing a natural infrared regulator of the theory. We find that the one-loop effective Coulomb field calculated using this varepsilon vanishes. The other scheme combines an infrared momentum cutoff with smearing of the delta-functions in the interaction vertices. We prove that this regularization admits factorization of the infrared contributions in multi-loop diagrams, and sum the corresponding infinite series. The effective electromagnetic field is found to vanish in this case too. An essentially perturbative nature of this result is emphasized and discussed in connection with the long-range expansion of the effective field.