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arXiv:1703.06730 · Theoretical and Mathematical Physics

A concise review of pseudobosons, pseudofermions, and their relatives

F. Bagarello

Published Nov 1, 2017• 10 citations
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Abstract

We review some basic definitions and a few facts recently established for D-pseudobosons and pseudofermions. We also discuss an extended version of pseudofermions based on biorthogonal bases in a finitedimensional Hilbert space and describe some examples in detail.
DOI
10.1134/s0040577917110083

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In a recent paper we have considered an explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. We have introduced the so-called pseudobosons, and the role of Riesz bases in this context has been analyzed in detail. In this paper we consider a general construction of pseudobosons based on an explicit coordinate representation, extending what is usually done in ordinary supersymmetric quantum mechanics. We also discuss an example arising from a linear modification of standard creation and annihilation operators, and we analyze its connection with coherent states.
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