Scalar Field in Non-commutative Curved Space Time

TL;DR

This paper investigates complex scalar field theories in noncommutative curved spacetime using a new star-product, deriving equations of motion and energy-momentum tensor under specific assumptions about noncommutativity and metric independence.

Contribution

It introduces a new star-product for noncommutative curved spacetime and derives key field equations assuming time-independent noncommutative parameters and metric.

Findings

Derived equations of motion for scalar fields in NCCST

Formulated the energy-momentum tensor in static NCCST

Assumed noncommutative parameters are spacetime-independent

Abstract

We study the issue of complex scalar field theories in noncommutative curved space time (NCCST) with a new star-product. In this paper, the equation of motion of scalar field and the canonical energy-momentum tensor of scalar field in static noncommutative curved space time (SNCCST) will be found. The most important point is the assumption of the noncommutative parameter ($\theta$) be $x^{\m}$-independent, the noncommutativity with time attended (TNC) and the metric tensor is time independent.