Quantum mechanics of a point particle in (2+1)-dimensional gravity

被引:144
作者
Matschull, HJ [1 ]
Welling, M [1 ]
机构
[1] Univ Utrecht, Inst Theoret Phys, NL-3584 CC Utrecht, Netherlands
关键词
D O I
10.1088/0264-9381/15/10/008
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We study the phase space structure and the quantization of a pointlike particle in (2 + 1)-dimensional gravity. By adding boundary terms to the first-order Einstein-Hilbert action, and removing all redundant gauge degrees of freedom, we arrive at a reduced action for a gravitating particle in 2+1 dimensions; which is invariant under Lorentz transformations and a group of generalized translations. The momentum space of the particle turns out to be the group manifold SL(2). Its position coordinates have non-vanishing Poisson brackets, resulting in a non-commutative quantum spacetime. We use the representation theory of SL(2) to investigate its structure. We find a discretization of time, and some semi-discrete structure of space. An uncertainty relation forbids a fully localized particle. The quantum dynamics is described by a discretized Klein-Gordon equation.
引用
收藏
页码:2981 / 3030
页数:50
相关论文
共 23 条
[1]   A CHERN-SIMONS ACTION FOR 3-DIMENSIONAL ANTI-DESITTER SUPERGRAVITY THEORIES [J].
ACHUCARRO, A ;
TOWNSEND, PK .
PHYSICS LETTERS B, 1986, 180 (1-2) :89-92
[2]  
[Anonymous], 1991, REPRESENTATION LIE G
[3]   Solving the N-body problem in (2+1) gravity [J].
Bellini, A ;
Ciafaloni, M ;
Valtancoli, P .
NUCLEAR PHYSICS B, 1996, 462 (2-3) :453-490
[4]   EXACT QUANTUM SCATTERING IN 2+1 DIMENSIONAL GRAVITY [J].
CARLIP, S .
NUCLEAR PHYSICS B, 1989, 324 (01) :106-122
[5]  
CARLIP S, 1993, GRQC9305020
[6]  
DIJKGRAAF R, 1992, NUCL PHYS B, V371, P269, DOI 10.1016/0550-3213(92)90237-6
[7]  
DMEICHEV A, 1997, HEPTH9701079
[8]   GRAVITY AND THE POINCARE GROUP [J].
GRIGNANI, G ;
NARDELLI, G .
PHYSICAL REVIEW D, 1992, 45 (08) :2719-2731
[9]   COMPLEX ANGULAR MOMENTA AND GROUPS SU(1,1) AND SU(2) [J].
HOLMAN, WJ ;
BIEDENHA.LC .
ANNALS OF PHYSICS, 1966, 39 (01) :1-&
[10]   CONTINUOUS DEGENERATE REPRESENTATIONS OF NONCOMPACT ROTATION GROUPS .2. [J].
LIMIC, N ;
NIEDERLE, J ;
RACZKA, R .
JOURNAL OF MATHEMATICAL PHYSICS, 1966, 7 (11) :2026-&