q-Supersymmetric Generalization of von Neumann's Theorem

TL;DR

This paper proves a q-supersymmetric extension of von Neumann's theorem, showing that all irreducible representations of the q-superoscillator algebra are equivalent via a superunitary transformation, generalizing a fundamental uniqueness result.

Contribution

It introduces a q-supersymmetric generalization of von Neumann's theorem, establishing the equivalence of irreducible representations of the q-superoscillator algebra.

Findings

All irreducible representations are equivalent via a superunitary transformation.

Provides a foundational result for q-supersymmetric quantum systems.

Extends von Neumann's theorem to q-deformed supersymmetric contexts.

Abstract

Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This provides with a q-supersymmetric generalization of the well-known uniqueness theorem of von Neumann for any finite number of degrees of freedom.