Field Theory with Coordinate Dependent Noncommutativity
Abstract
We discuss the formulation of classical field theoretical models on -dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field theories in noncommutative space-time to obtain local conservation laws (for the electric charge and for the energy-momentum tensor of free fields) and more generally an energy-momentum balance equation for interacting fields. For free field models an analogy with the damped harmonic oscillator in classical mechanics is pointed out, which allows us to get a physical understanding for the obtained conservation laws. To conclude, the formulation of field theories on curved noncommutative space is addressed.
Cite
@article{arxiv.1806.02131,
title = {Field Theory with Coordinate Dependent Noncommutativity},
author = {Daniel N. Blaschke and Francois Gieres and Stefan Hohenegger and Manfred Schweda and Michael Wohlgenannt},
journal= {arXiv preprint arXiv:1806.02131},
year = {2018}
}
Comments
Dedicated to the memory of Manfred Schweda who initiated this work, V2: References added. V3: Comments on the symmetries underlying the conservation laws added, V4: Published version