Two-dimensional model of interaction of a non-relativistic particle with scalar mesons in the strong coupling limit

TL;DR

This paper develops a two-dimensional nonrelativistic model of particle-scalar meson interactions in the strong coupling limit, introducing Bogolyubov transformations and a perturbation theory to analyze scattering properties.

Contribution

It introduces Bogolyubov transformations into the model and constructs a translation-invariant perturbation theory in inverse coupling, providing new analytical tools for strong coupling interactions.

Findings

Transmission and reflection coefficients are calculated.

The S-matrix is expressed in a holomorphic form.

Matrix elements of the interaction are explicitly computed.

Abstract

Bogolyubov transformations are introduced into the nonrelativistic model of particle interaction with scalar mesons. Within the framework of the generalized Hamiltonian formalism developed by Dirac, a translation-invariant perturbation theory in inverse powers of the coupling constant is constructed. Transmission and reflection coefficients are obtained, the S-matrix is written in a holomorphic representation, and the matrix element is calculated.