Proper-Time Formalism in a Constant Magnetic Field at Finite Temperature and Chemical Potential

Abstract

We investigate scalar and spinor field theories in a constant magnetic field at finite temperature and chemical potential. In an external constant magnetic field the exact solution of the two-point Green functions are obtained by using the Fock–Schwinger proper-time formalism. We extend it to the thermal field theory and find the expressions of the Green functions exactly for the temperature, the chemical potential and the magnetic field. For practical calculations the contour of the proper-time integral is carefully selected. The physical contour is discussed in a constant magnetic field at finite temperature and chemical potential. As an example, behavior of the vacuum self-energy is numerically evaluated for the free scalar and spinor fields.

Regularization dependence on phase diagram in Nambu–Jona-Lasinio model

“…Therefore, in this paper, we persistently use the latter way shown in Eq. (25) so that the model treatment becomes consistent. It should be noticed that the finite temperature correction, V T , contains no divergent integral.…”

“…The dimensional regularization analytically continues the spacetime dimension in the loop integrals to a non-integer value, then try to obtain finite contribution from the integrals [14]. Beside from the frequently used 3D cutoff way, there have been a lot of works by using the 4D [6,7], PV [6,[15][16][17], PT [6,[18][19][20][21][22][23][24][25][26], and DR [27][28][29][30][31][32]. Thus, the physical consequences depend on the regularization [34].…”

Quantum field theoretical structure of electrical conductivity of cold and dense fermionic matter in the presence of a magnetic field

“…Present work indicates a possibility of this phenomena in compact star environment, where also a strong magnetic field is expected in dense matter. It has also been seen that, SdH oscillations affect the transport and thermodynamic properties of the material [53]. It was shown in Ref.…”

“…(1), T is the time-ordering with respect to the symmetric Schwinger-Keldysh contour in the complex time plane (shown in Fig. 1) as used in the RTF of finite temperature field theory [53,[56][57][58][59][60][61], and, the subscript '11 ′ refers to the fact that the two points are on the real horizontal segment of . The explicit form of the current ( ) reads ( ) = .…”

“…[41] via RTA methods with Landau quantization, while present article is revealing the same possibility via quantum field theoretical methods, carrying some enriched structure. With the help of Schwinger's proper time methods [46][47][48][49][50][51][52][53][54][55] and the real time formalism (RTF) of thermal field theory [56][57][58][59][60][61][62], we have calculated the vector current-current correlation function involving Fermionic fields, whose zero momentum limit, based on Kubo-Zubarev formalism [63][64][65][66], provide a rich field theoretical expression of conductivity.…”