(1) Instituto de Física, Universidade de Brasília, Brasília, DF, 70910-900, Brasil;(2) Instituto de Física, Universidade Federal da Bahia, Campus de Ondina, Salvador, Bahia, 40210-340, Brasil
Abstract:
We apply the Galilean covariant formulation of quantum dynamics to derive the phase-space representation of the Pauli–Schrödinger 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.