Fields and strings on non commutative q-deformed spaces

TL;DR

This paper develops a framework for scalar field and string theories on non-commutative q-deformed spaces, introducing a product analogous to the Moyal product and exploring symmetry enhancements and gravitational implications.

Contribution

It defines a new product for functions on q-deformed spaces and provides a general method to formulate scalar and string theories in this setting, highlighting symmetry and gravitational effects.

Findings

Introduction of a q-deformed product analogous to Moyal product

Procedure for defining scalar and string theories on q-deformed spaces

Enlarged spacetime and internal symmetries in the resulting theories

Abstract

We study scalar field and string theory on non commutative q-deformed spaces. We define a product of functions on a non commutative algebra of functions resulting from the q-deformation analogue to the Moyal product for canonically non commutative spaces. We then give the general procedure to define scalar field and classical string theories on the mentioned spaces, we argue that the resulting theories will have enlarged sets of both spacetime and internal symmetries which can be used to study gravitational effects due to the q-deformation.