dorsal/arxiv
View SchemaDeformed Harmonic Oscillator Algebras defined by their Bargmann representations
| Authors | M. Irac-Astaud, G. Rideau |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9712043 |
| URL | https://arxiv.org/abs/q-alg/9712043 |
Abstract
Deformed 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: $[a,N] = a, [a^\dagger, N]= -a^\dagger, a^\dagger a = \psi(N)$ and $aa^\dagger =\psi(N+1)$. 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.
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"abstract": "Deformed Harmonic Oscillator Algebras are generated by four operators, two\nmutually adjoint $a$ and $a^\\dagger$, and two self-adjoint $N$ and the unity\n$1$ such as:\n $[a,N] = a, [a^\\dagger, N]= -a^\\dagger, a^\\dagger a = \\psi(N)$ and\n$aa^\\dagger =\\psi(N+1)$.\n The Bargmann Hilbert space is defined as a space of functions, holomorphic in\na ring of the complex plane, equipped with a scalar product involving a true\nintegral. In a Bargmann representation, the operators of a Deformed Harmonic\nOscillator Algebra act on a Bargmann Hilbert space and the creation (or the\nannihilation operator) is the multiplication by $z$.\n We discuss the conditions of existence of Deformed Harmonic Oscillator\nAlgebras assumed to admit a given Bargmann representation.",
"arxiv_id": "q-alg/9712043",
"authors": [
"M. Irac-Astaud",
"G. Rideau"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Deformed Harmonic Oscillator Algebras defined by their Bargmann representations",
"url": "https://arxiv.org/abs/q-alg/9712043"
},
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"id": "arXiv Dataset IDs",
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