Electrically neutral Dirac particles in the presence of external fields: Exact solutions

Abstract

In the present article we present exact solutions of the Dirac equation for electric neutral particles with anomalous electric and magnetic moments. Using the algebraic method of separation of variables, the Dirac equation is separated in cartesian, cylindrical and spherical coordinates, and exact solutions are obtained in terms of special functions. Typeset using REVT E X

Solution of the Dirac equation with magnetic monopole and pseudoscalar potentials

“…The series (26) will have good behavior at infinity if they terminate for a finite value N [35,36]. So we assume…”

Forward cone quantization of the Dirac field in “longitudinal boost-invariant” coordinates with cylindrical symmetry

“…This then produces a representation which we will connote the "diagonal tetrad" representation. To obtain the diagonal tetrad representation, one introduces a similarity transformation, S, such that 11) where the gamma matricesγ a are proportional to the constant gamma matrices, γ a . By construction, the two set of gamma matrices,γ a andγ a , are defined such that …”

“…This problem was also later considered by Parker [9] and collaborators who were interested in the problem of particle creation in expanding universes. More recently, Viallalba and coworkers have concerned themselves with the general problem of separation of variables [10] in external vector fields in order to find exact solutions [11] of the Dirac equation. The problem of quantizing the Dirac equation on the hyperboloids τ = (t 2 −x 2 −y 2 −z 2 ) 1/2 was also studied in great detail in the 1970's by Sommerfield [12], diSessa [13] and others [14].…”

Quasi-exact solvability of Dirac?Pauli equation and generalized Dirac oscillators

“…Another interesting system involving neutral fermions is the Dirac oscillator, which is of considerable interest in quantum chromodynamics [16]. However, unlike the case with minimal coupling, studies in exact solutions of the Dirac equations with non-minimal couplings are rather scanty [17,18,19], not to mention studies in quasi-exact solutions of these systems. Only recently, efforts have been directed to exploring certain structure relating to such systems.…”