
Abstract 
1 
Introduction 
2 
GaugeTheoretic 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 Wheeler–DeWitt
equation 

2.14 
The role of diffeomorphisms 

2.15 
The volume operator 

2.16 
The
real dynamics 

2.17 
Summary 
3 
Quantum Regge Calculus 

3.1 
Path
integral for Regge calculus 

3.2 
Higherderivative terms 

3.3 
First
simulations 

3.4 
The phase structure 

3.5 
Influence of the measure 

3.6 
Evidence
for a secondorder transition? 

3.7 
Avoiding collapse 

3.8 
Twopoint
functions 

3.9 
Nonhypercubic lattices 

3.10 
Coupling to SU(2)gauge
fields 

3.11 
Coupling to scalar matter 

3.12 
Recovering the Newtonian
potential 

3.13 
Gauge invariance in Regge calculus? 

3.14 
Assorted
topics 

3.15 
Summary 
4 
Dynamical triangulations 

4.1 
Introduction 

4.2 
Path
integral for dynamical triangulations 

4.3 
Existence of an exponential
bound? 

4.4 
Performing the state sum 

4.5 
The phase structure 

4.6 
Evidence for
a secondorder transition? 

4.7 
Influence of the measure 

4.8 
Higherderivative
terms 

4.9 
Coupling to matter fields 

4.10 
Nonspherical lattices 

4.11 
Singular
configurations 

4.12 
Renormalization group 

4.13 
Exploring geometric
properties 

4.14 
Twopoint functions 

4.15 
Summary 
5 
Conclusions and
Outlook 

Acknowledgements 

References 