Exact Green function for neutral Pauli-Dirac particle with anomalous magnetic momentum in linear magnetic field

It is shown that the propagator of the neutral Pauli-Dirac particle with an anomalous magnetic moment μ in an external linear magnetic field B(x)=B+B′x is the causal Green function Sc(xb,xa) of the Pauli-Dirac equation. The corresponding Green function is calculated via path integral method in global projection, giving rise to the exact eigenspinor expressions. The effective action is used to explicitly determine the production rate in vacuum of neutral Dirac particle in terms of B′ and μ, which is B independent.