Oscillator Quantum Algebra and Deformed su(2) Algebra
Harunobu Kubo
TL;DR
This paper introduces a difference operator realization of a quantum deformed oscillator algebra with a Casimir operator, linking it to deformed su(2) algebra and exploring applications to cyclic representations and Bloch electron problems.
Contribution
It presents a novel difference operator realization of the quantum deformed oscillator algebra with Casimir freedom and establishes its connection to deformed su(2) algebra.
Findings
Realization of $H_q(1)$ with Casimir operator freedom
Mapping to deformed quantum su(2) algebra
Potential application to Bloch electron analysis
Abstract
A difference operator realization of quantum deformed oscillator algebra with a Casimir operator freedom is introduced. We show that this have a nonlinear mapping to the deformed quantum su(2) which was introduced by Fujikawa et al. We also examine the cyclic representation obtained by this difference operator realization and the possibility to analyze a Bloch electron problem by .
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