Abstract
We have systematically constructed the general structure of the fermion self-energy and the effective quark propagator in the presence of a nontrivial background such as a hot magnetized 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 analyzed the fermion dispersion spectra in a hot magnetized 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 the presence of a 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 magnetized medium corresponding to QED and QCD with background magnetic field.
Highlights
In noncentral heavy ion collision (HIC) experiments in LHC at CERN and in RHIC at BNL, it is believed that a very strong magnetic field is created in the direction perpendicular to the reaction plane due to the spectator particles that are not participating in the collisions
The general structure of fermionic selfenergy for a chirally invariant theory has been formulated for a hot and magnetized medium. Using this we have obtained a closed form of the general structure of the effective fermion propagator
The collective excitations in such a nontrivial background have been obtained for timelike momenta in the weak-field and hard thermal loop (HTL) approximation in the domain m2thð∼g2T2 < jqfBj < T2
Summary
In noncentral heavy ion collision (HIC) experiments in LHC at CERN and in RHIC at BNL, it is believed that a very strong magnetic field is created in the direction perpendicular to the reaction plane due to the spectator particles that are not participating in the collisions. This reorganized perturbation theory, known as HTL perturbation theory (HTLpt), leads to gauge-independent results for various physical quantities [49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65] Within this one-loop HTLpt, the thermomagnetic correction to the quark self-energy [66], quark-gluon three-point [66] function at zero chemical potential, and four-point [67] function at finite chemical potential in the weak-field limit have been computed. We construct the general structure of the fermionic two-point functions (e.g., selfenergy and the effective propagator) in a nontrivial background such as a hot magnetized medium. We set the notation and briefly outline the fermionic propagator in the presence of a background magnetic field following Schwinger formalism [38]. We further note that in the absence of a heat bath, (11) reduces to (9), which is not obvious by inspection but we would see later
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