# Exact Green Function for Neutral Pauli-Dirac Particle with Anomalous Magnetic Momentum in Linear Magnetic Field

## TL;DR

This paper derives the exact Green function for a neutral Pauli-Dirac particle with an anomalous magnetic moment in a linear magnetic field, providing explicit eigenspinors and analyzing particle creation probabilities.

## Contribution

It presents the first exact calculation of the Green function for this system using path integral methods, including explicit eigenspinors and creation probability analysis.

## Key findings

- Exact Green function derived for the system
- Explicit eigenspinors obtained
- Particle creation probability analyzed as a function of field and magnetic moment

## Abstract

We consider Pauli--Dirac fermion submitted to an inhomogeneous magnetic field. It is showed that the propagator of the neutral Dirac particle with an anomalous magnetic moment in an external linear magnetic field is the causal Green function $S^{c}(x_{b},x_{a})$ of the Pauli--Dirac equation. The corresponding Green function is calculated via path integral method in global projection, giving rise to the exact eigenspinors expressions. The neutral particle creation probability corresponding to our system is analyzed, which is obtained as function of the introduced field $B'$ and the additional spin magnetic moment $\mu$.