Quantum kappa-deformed differential geometry and field theory

TL;DR

This paper develops quantum differential geometry tools in kappa-Minkowski noncommutative spacetime and applies them to formulate a covariant energy-momentum tensor for complex scalar fields.

Contribution

It introduces foundational geometric tools in kappa-Minkowski spacetime and constructs a covariant energy-momentum tensor for scalar field theory.

Findings

Established bicovariant differential calculus in kappa-Minkowski

Constructed a covariant energy-momentum tensor

Proved conservation via closedness of a four-form

Abstract

I introduce in kappa-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-star and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.