Generalization of Agranovich-Toshich transformation and constraint free bosonic representation for systems of truncated oscillators

TL;DR

This paper extends the Agranovich-Toshich transformation to higher-rank truncated oscillators, providing a new constraint-free bosonic representation and functional integral methods for analyzing thermodynamics and long-range order.

Contribution

It introduces a generalized Agranovich-Toshich transformation for higher-rank truncated oscillators and develops a constraint-free bosonic framework for such systems.

Findings

New constraint-free bosonic representation for truncated oscillators

Functional integral formulations for thermodynamic analysis

Application to long-range order investigations

Abstract

The generalization of Agranovich-Toshich representation of paulion operators in terms of bosonic ones for the case of truncated oscillators of higher ranks is represented. We use this generalization to introduce a new constraint free bosonic description of truncated oscillator systems. The corresponding functional integral representations for thermodynamic quantities are given and the application to investigations of Long Rang Order in the system is discussed.