Properties of neutral mesons in a hot and magnetized quark matter: Size-dependent effects

The Eigenfunction Method to Calculate the Klein-Gordon Propagator in an Inhomogeneous Magnetic Field

“…In addition, b factors relatively larger reinforce the decrease in the mass parameter M. The system temperature T also makes this parameter smaller. In fact, this last result is well known at constant magnetic fields [21][22][23].…”

“…)ϕ 4 , being λ 0 the coupling constant and ϕ the bosonic field, we can use the following expression [21] ) is the propagator in momenta space, without magnetic and temperature effects. Thermal effects over the system are including by Matsubara prescription [22,23] ; , 2…”

Integrals Involving Jacobi Theta Functions and Applications in Quantum Systems

“…( 7): (10) Remembering that the gamma function of argument ν and the modified Bessel function of the second kind of order ν, have the following representations [20] (11) (12) the Eq. ( 10) reads (13) Carrying out steps completely similar to what we did for I 2 , we find the expressions (14) For i = 3, we obtain (15) and finally (16) In the next section, we apply I 2 and I 3 to an interacting quantum gas of fermions and bosons, respectively.…”

“…However, these integrals are only tractable from a numerical point of view (up to our knowledge). Indeed, the integrals involving the Jacobi theta functions that appear in QFT acquire infinite values for the argument s → 0, thus requiring a regularization process of these integrals, for a later solution numeric [11][12][13].…”

Charged scalar field propagator under an external magnetic field: a connection between eigenfunction and proper time methods

“…The presence of these magnetic fields on the physical systems brings a series of interesting phenomena to be analyzed, namely: magnetic catalysis (MC) [5][6][7][8][9][10], inverse magnetic catalysis (IMC) [11][12][13][14][15][16][17], and breaking-restoration of chiral symmetry [18,19]. A mesonic system under an external magnetic background also was considered in [20][21][22][23]. In the finite size context, we have found that the magnetic field produces the direct and inverse catalysis effects in the Gross-Neveu model in the Refs.…”