机构:
Rudjer Boskovic Inst, HR-10002 Zagreb, CroatiaCtr Phys Theor, F-13288 Marseille, France
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.