Invariance properties of the Dirac equation with external electro-magnetic field

摘要

In this paper, we attempt to obtain the nature of the external field such that the Dirac equation with external electro-magnetic field is invariant. The Poincare group, which is the maximal symmetry group for field free case, is constrained by the presence of the external field. Introducing infinitesimal transformation of x and Ψ, we apply Lie's extended group method to obtain the class of external field which admit of the invariance of the equation. It is important to note that the constraints for the existence of invariance are explicity on the electric and magnetic field, though only potentials explicity appears in the equation.