English

Algebras with convergent star products and their representations in Hilbert spaces

Mathematical Physics 2013-12-24 v1 High Energy Physics - Theory Functional Analysis math.MP Quantum Algebra

Abstract

We study star product algebras of analytic functions for which the power series defining the products converge absolutely. Such algebras arise naturally in deformation quantization theory and in noncommutative quantum field theory. We consider different star products in a unifying way and present results on the structure and basic properties of these algebras, which are useful for applications. Special attention is given to the Hilbert space representation of the algebras and to the exact description of their corresponding operator algebras.

Keywords

Cite

@article{arxiv.1312.6571,
  title  = {Algebras with convergent star products and their representations in Hilbert spaces},
  author = {Michael A. Soloviev},
  journal= {arXiv preprint arXiv:1312.6571},
  year   = {2013}
}

Comments

LaTeX, 17 pages, no figures