Gauge invariance of the Dirac equation

Abstract

The Dirac equation in its most usual form can be derived by the minimum action principle from the Lagrangian density where γk (k =1,2,3,4) are the Dirac 4 × 4 matrices satisfying relations; ψ(x) is a column matrix with 4 complex elements being functions of x1, x2, x3, x4, coordinates of the pseudo-Euclidean space with metric gik.(