Deformed Harmonic Oscillator Algebras defined by their Bargmann representations

Simple item page
dc.creatorIrac-Astaud, M.
dc.creatorRideau, G.
dc.date1997-12-17
dc.date.accessioned2026-07-07T05:57:47Z
dc.date.available2026-07-07T05:57:47Z
dc.descriptionDeformed Harmonic Oscillator Algebras are generated by four operators, two mutually adjoint $a$ and $a^\dagger$, and two self-adjoint $N$ and the unity $1$ such as: $[a,N] = a, [a^\dagger, N]= -a^\dagger, a^\dagger a = ψ(N)$ and $aa^\dagger =ψ(N+1)$. The Bargmann Hilbert space is defined as a space of functions, holomorphic in a ring of the complex plane, equipped with a scalar product involving a true integral. In a Bargmann representation, the operators of a Deformed Harmonic Oscillator Algebra act on a Bargmann Hilbert space and the creation (or the annihilation operator) is the multiplication by $z$. We discuss the conditions of existence of Deformed Harmonic Oscillator Algebras assumed to admit a given Bargmann representation.
dc.description27 pages, Latex
dc.identifierhttps://arxiv.org/abs/q-alg/9712043
dc.identifierhttp://arxiv.org/abs/q-alg/9712043
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/88116
dc.subjectQuantum Algebra
dc.titleDeformed Harmonic Oscillator Algebras defined by their Bargmann representations
dc.typetext

Files

Collections

arXiv