Noncommutative fields and actions of twisted Poincare algebra

Journal Article · Tue Apr 15 04:00:00 EDT 2008 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2907580· OSTI ID:21100257

Chaichian, M; Tureanu, A ^[1]; Kulish, P P ^[1]; Zhang, R B ^[2]; Xiao, Zhang ^[3]

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1. Department of Physics, University of Helsinki and Helsinki Institute of Physics, P.O. Box 64, 00014 Helsinki (Finland)
2. School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006 (Australia)
3. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences 100190, Beijing (China)

Within the context of the twisted Poincare algebra, there exists no noncommutative analog of the Minkowski space interpreted as the homogeneous space of the Poincare group quotiented by the Lorentz group. The usual definition of commutative classical fields as sections of associated vector bundles on the homogeneous space does not generalize to the noncommutative setting, and the twisted Poincare algebra does not act on noncommutative fields in a canonical way. We make a tentative proposal for the definition of noncommutative classical fields of any spin over the Moyal space, which has the desired representation theoretical properties. We also suggest a way to search for noncommutative Minkowski spaces suitable for studying noncommutative field theory with deformed Poincare symmetries.

• OSTI ID: 21100257
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 4 Vol. 49; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
COMMUTATION RELATIONS
LORENTZ GROUPS
MINKOWSKI SPACE
QUANTUM FIELD THEORY
SPIN
SYMMETRY
VECTORS