Scalar field theory on noncommutative Snyder spacetime
- Centre de Physique Theorique, Case 907 Luminy, 13288 Marseille (France)
- Rudjer Boskovic Institute, Bijenicka c.54, HR-10002 Zagreb (Croatia)
We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincare group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.
- OSTI ID:
- 21410132
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevD.82.024028; (c) 2010 The American Physical Society; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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