Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity

被引:11
作者
Bonzom, Valentin [1 ]
Laddha, Alok [2 ]
机构
[1] Perimeter Inst Theoret Phys, 31 Caroline St N, Waterloo, ON N2L 2Y5, Canada
[2] Penn State Univ, Inst Gravitat & Cosmos, University Pk, PA 16802 USA
关键词
Hamiltonian constraint; loop quantum gravity; parametrized field theories; topological BF theory; discrete gravity; MASTER CONSTRAINT PROGRAM; TOPOLOGY-CHANGING AMPLITUDES; PARAMETRIZED SCALAR FIELD; SPIN DYNAMICS; GAUGE-THEORIES; ASYMPTOTICS; INVARIANT; QSD; STATISTICS; PONZANO;
D O I
10.3842/SIGMA.2012.009
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of the quantum Hamiltonian is presented, and then more recent approaches. They are based on toy models which provide new insights into the difficulties and ambiguities faced in Thiemann's construction. The models we use are parametrized field theories, the topological BF model of which a special case is three-dimensional gravity which describes quantum flat space, and Regge lattice gravity.
引用
收藏
页数:50
相关论文
共 119 条
[21]   Asymptotics of 4d spin foam models [J].
Barrett, John W. ;
Dowdall, Richard J. ;
Fairbairn, Winston J. ;
Gomes, Henrique ;
Hellmann, Frank ;
Pereira, Roberto .
GENERAL RELATIVITY AND GRAVITATION, 2011, 43 (09) :2421-2436
[22]   QUANTUM GRAVITY ASYMPTOTICS FROM THE SU(2) 15j- SYMBOL [J].
Barrett, John W. ;
Fairbairn, Winston J. ;
Hellmann, Frank .
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2010, 25 (14) :2897-2916
[23]   An algebraic interpretation of the Wheeler-DeWitt equation [J].
Barrett, JW ;
Crane, L .
CLASSICAL AND QUANTUM GRAVITY, 1997, 14 (08) :2113-2121
[24]   CANONICAL BF-TYPE TOPOLOGICAL FIELD-THEORY AND FRACTIONAL STATISTICS OF STRINGS [J].
BERGERON, M ;
SEMENOFF, GW ;
SZABO, RJ .
NUCLEAR PHYSICS B, 1995, 437 (03) :695-721
[25]   TOPOLOGICAL GAUGE-THEORIES OF ANTISYMMETRIC TENSOR-FIELDS [J].
BLAU, M ;
THOMPSON, G .
ANNALS OF PHYSICS, 1991, 205 (01) :130-172
[26]   A NEW CLASS OF TOPOLOGICAL FIELD-THEORIES AND THE RAY-SINGER TORSION [J].
BLAU, M ;
THOMPSON, G .
PHYSICS LETTERS B, 1989, 228 (01) :64-68
[27]  
Blohmann C., ARXIV10032857
[28]  
Bonzom V., ARXIV11033415
[29]  
Bonzom V., ARXIV12014996
[30]  
Bonzom V., ARXIV11081569