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

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 oneloop 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.

Anisotropic pressure of deconfined QCD matter in presence of strong magnetic field within one-loop approximation

“…However, for the gluonic case, this calculation assumes that the only effect of the magnetic field is to shift the Debye mass without any change in the general structure of two point functions at the finite temperature. It has explicitly been shown [38][39][40][41] that the presence of an external magnetic field breaks the rotational symmetry and the situation is quite different from what has been assumed in Ref. [22].…”

“…Various discrete symmetries of the effective two-point functions are discussed in detail in Ref. [40].…”

“…There are four modes, two come from L 2 = 0 and two from R 2 = 0. In LLL only two modes are allowed [40]:…”

“…In recent years numerous activities have been in progress such as magnetic catalysis [1][2][3], inverse magnetic catalysis [4][5][6][7][8][9][10][11][12] and chiral magnetic effect [13][14][15] at finite temperature, and the chiral-and color-symmetry broken/restoration phase [16][17][18][19][20]. Also in progress is the study related to the equation of state (EoS) in thermal perturbative QCD (pQCD) models [21,22], holographic models [23,24] and various thermodynamic properties [19,20,25,26], refractive indices and decay constant of hadrons [27][28][29][30][31][32][33][34]; soft photon production from conformal anomaly [35,36] in HIC; modification of dispersion properties in a magnetized hot QED [37,38] and QCD [38][39][40][41] medium; and various transport coefficients [42]…”

Soft contribution to the damping rate of a hard photon in a weakly magnetized hot medium

“…Various properties of QCD matter at weak coupling in presence of magnetic field is being studied including the equation of state [19][20][21], transport properties [22][23][24]. Modification of QCD Debye mass and the two point correlation functions of quarks [25] and gluons [26][27][28] i.e., partons have been analyzed recently. Dilepton production rate from a hot magnetized QCD plasma [29][30][31][32][33][34][35][36] has been calculated.…”