Galilean-Covariant clifford algebras in the phase-space representation

Abstract

We apply the Galilean covariant formulation of quantum dynamics to derive the phase-space representation of the Pauli–Schr¨odinger equation for the density matrix of spin-1/2 particles in the presence of an electromagnetic field. The Liouville operator for the particle with spin follows from using the Wigner– Moyal transformation and a suitable Clifford algebra constructed on the phase space of a (4+1)-dimensional space–time with Galilean geometry. Connections with the algebraic formalism of thermofield dynamics are also investigated.