Effective action for fermions with anomalous magnetic moment from Foldy-Wouthuysen transformation

TL;DR

This paper derives the effective action for neutral fermions with anomalous magnetic moments in external fields using the Foldy-Wouthuysen transformation, enabling explicit calculations of Hamiltonian, partition function, and thermodynamic potentials.

Contribution

It introduces a method to explicitly evaluate the diagonalized Hamiltonian for such systems, facilitating the calculation of effective actions and thermodynamic properties.

Findings

Explicit form of the effective action obtained

Partition function at finite temperature derived

Thermodynamical potentials calculable from the effective action

Abstract

In this paper we calculate the effective action for neutral particles with anomalous magnetic moment in an external magnetic and electric field. We show that we can take advantage from the Foldy Wouthuysen transformation for such systems, determined in our previous works: indeed, by this transformation we have explicitly evaluated the diagonalized Hamiltonian, allowing to present a closed form for the corresponding effective action and for the partition function at finite temperature from which the thermodynamical potentials can be calculated.