New results about the canonical transformation for boson operators

TL;DR

This paper presents a simple method to derive the analytical expression for the overlap matrix between basis states in the context of the Bogoliubov transformation for monopole bosons, facilitating the understanding of unitary transformations between boson Fock spaces.

Contribution

It introduces a straightforward analytical approach to compute the overlap matrix for basis states related by the Bogoliubov transformation in bosonic systems.

Findings

Derived an explicit analytical expression for the overlap matrix.

Simplified the process of connecting initial and correlated boson Fock spaces.

Enhanced understanding of the unitary transformation induced by the Bogoliubov transformation.

Abstract

The Bogoliubov transformation for a monopole boson induces an unitary transformation connecting the Fock spaces of initial and correlated boson-s. Here we provide a very simple method for deriving the analytical expression for the overlap matrix of the basis states generating the two boson spaces.