Noncommutative Parameters of Quantum Symmetries and Star Products

TL;DR

This paper explores how star products can translate noncommutative space-time symmetries into a framework involving classical functions, specifically focusing on $$-deformed Minkowski space and Poincar group.

Contribution

It extends the star product method to include noncommutative parameters of quantum symmetries, representing them as functions on the classical Poincar group.

Findings

Representation of noncommutative parameters by functions on classical Poincar group

Extension of star product to tensor products involving deformed spaces and groups

Framework for translating noncommutative symmetries into classical function space

Abstract

The star product technique translates the framework of local fields on noncommutative space-time into nonlocal fields on standard space-time. We consider the example of fields on $\kappa$- deformed Minkowski space, transforming under $\kappa$-deformed Poincar\'{e} group with noncommutative parameters. By extending the star product to the tensor product of functions on $\kappa$-deformed Minkowski space and $\kappa$-deformed Poincar\'{e} group we represent the algebra of noncommutative parameters of deformed relativistic symmetries by functions on classical Poincar\'{e} group.