On relativistic quantum theory for particles with spin1/2

Abstract

The authors study a family of Hilbert spaces with positive definite invariant scalar product for the quantum mechanical description of relativistic spin-1/2 particles. The Hermitian and anti-Hermitian parts of the Dirac operator gamma mu pmu are related to energy and helicity. Replacing pmu by pmu -eAmu , the difference between the squares of these operators provides a minimal coupling evolution operator, similar to the second-order Dirac operator, for which Fmu nu is coupled to a covariant form of the Pauli spin matrices which generate SU(2) in a space-like surface. No Dirac sea is required for the consistency of the theory.