Canonical quantization of a product within the Cahill-Glauber correspondence

Abstract

The (canonical) quantization of a product of two phase-space functions can be expressed as a commutative mapping between the quantizations of its factors. In this note, we discuss such a mapping within the Cahill-Glauber $s$-parameterized correspondence framework, providing a heuristic (hence less mathematically rigorous, but arguably more easily understood) derivation for the bidifferential form. The term "hatted star product" is coined by virtue of the structural similarity to the star product in phase space, a special case of which is the celebrated Moyal star product.

5 pages. Added more literature review. Improved clarity and scope of discussion. This is a technical note not planned for any journal submission