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

Abstract

In this paper, we use the Eigenfunction method (Ritus'method) to calculate the Klein-Gordon propagator under an external magnetic field with an exponential damping factor b, in a four-dimensional Euclidean space. We write the propagator of scalar field in terms of plane waves and Laguerre polynomials. Also the eigenvalues associated to differential operator show the quantization in the xy-plane through the Landau levels. We apply the calculated propagator to the mass parameter of an interacting boson system under an exponentially decaying magnetic field.

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

“…where ω ≡ |eB| is the cyclotron frequency. Thus, to solve the eigenvalue equation, we make the ansätze [35][36][37][38]…”

“…This method allows writing the propagator under an external field as in the free case, i.e., in a diagonal form. A few years ago, Ritus' method was considered in low dimensions to describe the graphene [33] and in QFT scenario [34][35][36][37].…”