Computing the normalized dirac wave function for oblique electric and magnetic fields

Abstract

Interactions taking place in superstrong gravitational and magnetic fields can account for a wide variety of spectral emissions from compact objects such as neutron stars. A quantum treatment of the particle transport in these environments,e.g., needed to calculate the anisotropic electrical conductivity, depends on the evaluation of matrix elements with solutions to the Dirac equation in oblique electric (E) and magnetic (H) fields. However, due to the complexity of the bispinors, these overlap integrals are often extremely difficult to compute. Indeed, no normalized wave function yet exists. Here we show that, in the special case whenE/H≲10−4, a simplification of the matrix elements permits an analytic integration that yields explicit expressions for the normalization constant and other overlap integrals. Physical quantities, such as the conductivity tensor, that depend directly on these matrix elements may then be computed in a straightforward way.