Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 133, 35 pages      arXiv:1806.02131      https://doi.org/10.3842/SIGMA.2018.133

Field Theory with Coordinate Dependent Noncommutativity

Daniel N. Blaschke a, François Gieres b, Stefan Hohenegger b, Manfred Schweda c and Michael Wohlgenannt d
a) Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
b) Institut de Physique Nucléaire de Lyon, Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Bat. Paul Dirac, 4 rue Enrico Fermi, F-69622-Villeurbanne, France
c) Deceased
d) Austro-Ukrainian Institute for Science and Technology c/o AUI, ITP, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria

Received September 19, 2018, in final form December 11, 2018; Published online December 23, 2018

Abstract
We discuss the formulation of classical field theoretical models on $n$-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.

Key words: NCQFT; energy-momentum tensor; noncommutative geometry.

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