Imaginary-time path integral for a relativistic spin-(1/2) particle in a magnetic field

We construct a Feynman-Kac-Ito formula for positive-energy spin-(1/2) relativistic particles in a purely magnetic external field. We also introduce a new class of quantum Hamiltonians, the <<relativistic Pauli operators>>, along with a path integral representation of their semi-groups. These Hamiltonians differ from the relativistic Schrodinger operators of Carmona, Masters and Simon only when a magnetic field is present.