Deformed Harmonic Oscillator Algebras defined by their Bargmann representations
q-alg
2007-05-23 v1 Quantum Algebra
Abstract
Deformed Harmonic Oscillator Algebras are generated by four operators, two mutually adjoint and , and two self-adjoint and the unity such as: and . 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 . We discuss the conditions of existence of Deformed Harmonic Oscillator Algebras assumed to admit a given Bargmann representation.
Cite
@article{arxiv.q-alg/9712043,
title = {Deformed Harmonic Oscillator Algebras defined by their Bargmann representations},
author = {M. Irac-Astaud and G. Rideau},
journal= {arXiv preprint arXiv:q-alg/9712043},
year = {2007}
}
Comments
27 pages, Latex