Quantum κ-deformed differential geometry and field theory

Abstract

I introduce in [Formula: see text]-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-[Formula: see text] 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.