Abstract
1
Introduction
2
Gauge-theoretic discretizations of gravity
2.1
Lagrangian treatment. Introduction
2.2
Smolin's lattice model
2.3
Numerical implementation
2.4
Other gauge formulations
2.5
Proving reflection positivity
2.6
The measure
2.7
Assorted topics
2.8
Summary
2.9
Hamiltonian treatment. Introduction
2.10
Hamiltonian lattice gravity
2.11
The measure
2.12
The constraint algebra
2.13
Solutions to the ...
2.14
The role of ...
2.15
The volume operator
2.16
The real dynamics
2.17
Summary
3
Quantum Regge Calculus
3.1
Path integral for ...
3.2
Higher-derivative terms
3.3
First simulations
3.4
The phase structure
3.5
Influence of the ...
3.6
Evidence for a ...
3.7
Avoiding collapse
3.8
Two-point functions
3.9
Non-hypercubic lattices
3.10
Coupling to SU(2)-gauge ...
3.11
Coupling to scalar ...
3.12
Recovering the Newtonian ...
3.13
Gauge invariance in ...
3.14
Assorted topics
3.15
Summary
4
Dynamical triangulations
4.1
Introduction
4.2
Path integral for ...
4.3
Existence of an ...
4.4
Performing the state ...
4.5
The phase structure
4.6
Evidence for a ...
4.7
Influence of the ...
4.8
Higher-derivative terms
4.9
Coupling to matter ...
4.10
Non-spherical lattices
4.11
Singular configurations
4.12
Renormalization group
4.13
Exploring geometric properties
4.14
Two-point functions
4.15
Summary
5
Conclusions and Outlook
References