Oeckl R. Discrete Gauge Theory. From Lattices to TQFT 2005

Textbook in PDF format

This book provides an introduction to topological quantum field theory as well as discrete gauge theory with quantum groups. In contrast to much of the existing literature, the present approach is at the same time intuitive and mathematically rigorous, making extensive use of suitable diagrammatic methods. It provides a highly unified description of lattice gauge theory, topological quantum field theory and models of quantum (super)gravity. The reader is thus in a unique position to understand the relations between these subjects as well as the underlying groundwork.
Quantization of Discretized Gauge Theories
Topology: Decomposition of Manifolds
Categories and Diagrams
Representation Theory: Groups and Hopf Algebras
Cellular Gauge Theory
Topological Quantum Field Theory
Related Constructions
Applications to Lattice Models and Quantum Gravity