The book is devoted to the study of condensed matter systems dominated by defects and their long-range interactions. These interactions are described in terms of local fields and the relevant dynamics exhibits a gauge symmetry. The main idea underlying the book is that since it is almost hopeless to try to describe strongly nonlinear phenomena in condensed matter physics by carrying the perturbative expansion to all orders it is necessary to find a way of directly including the macroscopic excitations created by nonlinear effects.
The book is divided into four parts. The first one provides an introduction to standard field-theoretical methods in application to statistical physics. The functional methods are described, perturbation theory and low temperature expansion are discussed in some detail. The last chapter of this part is devoted to the study of random chains.
The second part contains a gauge field theoretic treatment of superfluid helium. The main idea is here that the superfluid phase transition may be understood as an infinite growth and proliferation of vortex lines. In order to make it possible to study ensembles of vortex lines at low and high densities the XY model is invoked mainly in the Villain approximation.
Part three is devoted to the study of melting processes of crystals in terms of gauge theory of defects. An important concept of disordered fields for ensembles of line-like defects is introduced. This theory has a natural way of undergoing a first-order phase transition already at the mean field level. It contains as many complex disorder parameters as there are lattice dimensions and describes a grand canonical ensemble of dislocations and disclinations.
In the last chapter the theory of gauge fields of defects in the continuum limit is discussed and the connection with a linearized theory of gravity in a metric space with curvature and torsion is pointed out.
The book covers a wide range of methods and techniques and contains a very detailed treatment of two important systems, superfluids and crystals. It is written in clear and interesting way and stresses the importance of field theoretical ideas and methods in the areas of condensed matter and solid state physics.