Bose Operators, Coherent States, Truncation, Spin Coherent States, Lie Algebras and Spectrum

TL;DR

This paper investigates the properties of truncated Bose operators in finite-dimensional spaces, comparing their spin coherent states with canonical coherent states, and analyzing their Lie algebra structure and spectrum.

Contribution

It introduces a detailed analysis of truncated Bose operators, highlighting their algebraic structure and spectral properties, and compares different types of coherent states.

Findings

Truncated Bose operators have distinct spectral characteristics.

Spin coherent states differ from canonical coherent states in this context.

Lie algebra structures of truncated operators are explicitly characterized.

Abstract

We study truncated Bose operators in finite dimensional Hilbert spaces. Spin coherent states for the truncated Bose operators and canonical coherent states for Bose operators are compared. The Lie algebra structure and the spectrum of the truncated Bose operators are discussed.