4 x 4 matrices in Dirac parametrization: inversion problem and determinant

Abstract

Parametrization of complex 4 x 4 - matrices G in terms of Dirac tensor parameters (A,B,A_{l},B_{l},F_{kl}) or equivalent four complex 4-vectors (k,m,n,l) is investigated. In the given parametrization, the problem of inverting any 4 x 4 matrix G is solved. Expression for determinant of any matrix G is found: det G = F(k,m,n,l).