Some classes of finite-dimensional ladder operators

2025/07/22 by Fabio Bagarello, Bagarello, Fabio, Antonino Faddetta +3
Mathematics · #Advanced Operator Algebra Research #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2507.16629

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce and study some special classes of ladder operators in finite-dimensional Hilbert spaces. In particular we consider a truncated version of quons, their \em psudo-version, and a third family of operators acting on a closed chain. In this latter situation, we discuss the existence of what could be considered \em discrete coherent states, as suitable eigenvectors of the annihilation operator of the chain. We see that, under reasonable assumptions, a resolution of the identity can be recovered, involving these states, together with a biorthogonal family of vectors, which turn out to be eigenstates of the raising operator of the chain.

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