Space-time symmetries of noncommutative spaces

Journal Article · Fri Apr 15 04:00:00 EDT 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.71.085012· OSTI ID:20709116

Calmet, Xavier ^[1]

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1. Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 (United States)

We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. The noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We show that the star product is invariant under noncommutative Lorentz transformations. We then apply our idea to the case of actions obtained by expanding the star product and the fields taken in the enveloping algebra via the Seiberg-Witten maps and verify that these actions are invariant under these new noncommutative Lorentz transformations. We finally consider general coordinate transformations and show that the metric is undeformed.

• OSTI ID: 20709116
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 71; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
COMMUTATION RELATIONS
LORENTZ TRANSFORMATIONS
QUANTUM FIELD THEORY
SPACE-TIME
SYMMETRY
VECTOR FIELDS