Functional Integral Representation for Relativistic Schrodinger Operator Coupled to a Scalar Bose Field with $P(\phi)$ Interaction

TL;DR

This paper derives a functional integral representation for a semi-relativistic particle interacting with a scalar Bose field under a $P()$ interaction, providing a mathematical framework for such quantum systems.

Contribution

It introduces a novel functional integral representation for the semi group of a semi-relativistic particle coupled to a scalar Bose field with $P()$ interaction.

Findings

Functional integral representation established for the Hamiltonian

Ultraviolet cutoff condition applied to the Bose field

Main theorem provides a rigorous mathematical framework

Abstract

In this paper the system of a semi-relativistic particle interacting with a scalar Bose field is investigated. The ultraviolet cutoff condition is imposed on the Bose field. In the main theorem, the functional integral representation of the semi group generated by the total Hamiltonian with $P(\phi)$ interaction is obtained.