Algebras with convergent star products and their representations in Hilbert spaces

Understand

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.