Dirac field and gravity in NC S O ( 2 , 3 ) ⋆ model

Action for the Dirac spinor field coupled to gravity on noncommutative (NC) Moyal-Weyl spacetime is obtained without prior knowledge of the metric tensor. We emphasize gauge origins of gravity and its interaction with fermions by demonstrating that a classical action invariant under SO(2, 3) gauge t...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2018-03, Vol.78 (3), p.1-14
Main Authors: Gočanin, Dragoljub, Radovanović, Voja
Format: Article
Language:English
Subjects:
Broken symmetry
Couplings
Deformation effects
Dirac equation
Electrons
Fermions
Gravitation
Invariants
Relativity
Spacetime
Symmetry
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Summary:Action for the Dirac spinor field coupled to gravity on noncommutative (NC) Moyal-Weyl spacetime is obtained without prior knowledge of the metric tensor. We emphasize gauge origins of gravity and its interaction with fermions by demonstrating that a classical action invariant under SO(2, 3) gauge transformations can be exactly reduced to the Dirac action in curved spacetime after breaking the original symmetry down to the local Lorentz SO(1, 3) symmetry. The commutative SO(2, 3) invariant action can be straightforwardly deformed via Moyal-Weyl ⋆-product to its NC SO(2,3)⋆ invariant version which can be expanded perturbatively in powers of the deformation parameter using the Seiberg-Witten map. The NC gravity-matter couplings in the expansion arise as an effect of the gauge symmetry breaking. We calculate in detail the first order NC correction to the classical Dirac action in curved spacetime and show that it does not vanish. Moreover, linear NC effects are apparent even in flat spacetime. We analyse NC deformation of the Dirac equation, Feynman propagator and dispersion relation for electrons in Minkowski spacetime and conclude that constant NC background acts as a birefringent medium for electrons propagating in it.
ISSN:1434-6044
1434-6052
DOI:10.1140/epjc/s10052-018-5669-4