On relativistic quantum theory for particles with spin ¹/₂

The authors study a family of Hilbert spaces with positive definite invariant scalar product for the quantum mechanical description of relativistic spin-¹/₂particles. The Hermitian and anti-Hermitian parts of the Dirac operator gamma^mup_muare related to energy and helicity. Replacing p^muby p^mu-eA^mu, the difference between the squares of these operators provides a minimal coupling evolution operator, similar to the second-order Dirac operator, for which F^{mu 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.