Scalar field theory on noncommutative Snyder spacetime

被引:76
|
作者
Battisti, Marco Valerio [1 ]
Meljanac, Stjepan [2 ]
机构
[1] Ctr Phys Theor, F-13288 Marseille, France
[2] Rudjer Boskovic Inst, HR-10002 Zagreb, Croatia
来源
PHYSICAL REVIEW D | 2010年 / 82卷 / 02期
关键词
KAPPA-MINKOWSKI; SPECIAL RELATIVITY; MODEL; TIME;
D O I
10.1103/PhysRevD.82.024028
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
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.
引用
收藏
页数:9
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