Boundary effects on constituent quark masses and on chiral susceptibility in a four-fermion interaction model

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

“…Concerning the spatial compactified coordinates, one can also use as a natural generalization the antiperiodic boundary conditions. In this case, however, it is worthy mentioning that there are no conceptual restrictions regarding their periodicity, as stressed in several works ( [35,58,[75][76][77]). This choice depends on the physical interest, and reverberate on the physical quantities obtained in the effective approach.…”

Integrals Involving Jacobi Theta Functions and Applications in Quantum Systems

“…( 9) in Eq. ( 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

“…[24,25] and [24,26], respectively. In the Nambu-Jona-Lasinio model, the IMC phenomenon at finite size was found in [27] and the MC considering finite size of the system was found in [4,28].…”