Generalized κ-DEFORMATIONS and Deformed Relativistic Scalar Fields on Noncommutative Minkowski Space

Details Generalized κ-DEFORMATIONS and Deformed Relativistic Scalar Fields on Noncommutative Minkowski Space Generalized κ-DEFORMATIONS and Deformed Relativistic Scalar Fields on Noncommutative Minkowski Space

Aug 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006tmpg.conf..255k&link_type=abstract

Topics in Mathematical Physics, General Relativity and Cosmology in Honor of Jerzy Plebański. Proceedings of 2002 International

Mathematics

Mathematical Physics

Scientific paper

We describe the generalized κ-deformations of D = 4 relativistic symmetries with finite masslike deformation parameter κ and an arbitrary direction in κ-deformed Minkowski space being noncommutative. The corresponding bicovariant differential calculi on κ-deformed Minkowski spaces are considered. Two distinguished cases are discussed: 5D noncommutative differential calculus (κ-deformation in time-like or space-like direction), and 4D noncommutative differential calculus having the classical dimension (noncommutative κ-deformation in light-like direction). We introduce also left and right vector fields acting on functions of noncommutative Minkowski coordinates, and describe the noncommutative differential realizations of κ-deformed Poincaré algebra. The κ-deformed Klein-Gordon field on noncommutative Minkowski space with noncommutative time (standard κ-deformation) as well as noncommutative null line (light-like κ-deformation) are discussed. Following our earlier proposal (see Refs. 1, 2) we introduce an equivalent framework replacing the local noncommutative field theory by the nonlocal commutative description with suitable nonlocal star product multiplication rules. The modification of Pauli-Jordan commutator function is described and the κ-dependence of its light-cone behaviour in coordinate space is explicitely given. The problem with the κ-deformed energy-momentum conservation law is recalled.

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