
I have written a book entitled Discrete Gauge Theory: From Lattices to TQFT. Its main subject is topological quantum field theory and its relation to lattice gauge theory and other models of physics. I extensively use circuit diagrams and a point of view inspired by lattice gauge theory to make the constructions as intuitive and geometrical as possible, especially with a mathematical physicist as a reader in mind. At the same time I sacrifice no mathematical rigour, hopefully making the book attractive also to the interested mathematician. The topological quantum field theories constructed are generalizations of the TuraevViro model (in dimension three) and the CraneYetter model (in dimension four). The construction is first performed as a generalization of lattice gauge theory using quantum groups and then specialized to the topological case. This is done using cellular moves, a generalization of Pachner moves to cellular decompositions of manifolds. Furthermore, the construction is performed first in a way applicable to manifolds of arbitrary dimension. Then, the low dimensional situation (2,3,4) is adapted to the specialities of topology in that dimension. This goes along with a corresponding choice of category. Applications discussed in the book include spin foam models of quantum gravity and quantum supergravity, nonabelian duality, spin models, generating field theory (generalized matrix models) and renormalization. 