General structure of fermion two-point function and its spectral representation in a hot magnetised medium

TL;DR

This paper develops a comprehensive framework for understanding fermion two-point functions and spectral properties in hot, magnetized media, applicable to QED and QCD, revealing symmetry behaviors and dispersion characteristics.

Contribution

It introduces a general structure for fermion self-energy and propagator in a hot magnetized medium, including spectral representation, applicable to both QED and QCD, and verifies it through one-loop calculations.

Findings

Fermion spectra reflect discrete symmetries of two-point functions.

Magnetic field causes separation of chiral modes without breaking chiral symmetry.

Spectral representation of two-point functions is explicitly computed.

Abstract

We have systematically constructed the general structure of the fermion self-energy and the effective quark propagator in presence of a nontrivial background like hot magnetised medium. This is applicable to both QED and QCD. The hard thermal loop approximation has been used for the heat bath. We have also examined transformation properties of the effective fermion propagator under some of the discrete symmetries of the system. Using the effective fermion propagator we have analysed the fermion dispersion spectra in a hot magnetised medium along with the spinor for each fermion mode obtained by solving the modified Dirac equation. The fermion spectra is found to reflect the discrete symmetries of the two-point functions. We note that for a chirally symmetric theory the degenerate left and right handed chiral modes in vacuum or in a heat bath get separated and become asymmetric in presence of magnetic field without disturbing the chiral invariance. The obtained general structure of the two-point functions is verified by computing the three-point function, which agrees with the existing results in one-loop order. Finally, we have computed explicitly the spectral representation of the two-point functions which would be very important to study the spectral properties of the hot magnetised medium corresponding to QED and QCD with background magnetic field.