QUANTUM FIELD-THEORY OF CRYSTALS AND EXTENDED OBJECTS

This is a review of the quantum field theory of crystals and extended objects. A quantum field theoretical treatment of crystals is presented from the view point of the spontaneous breakdown of the spatial translation invariance. It is proved that there exist at least three gapless Goldstone bosons which are identified as acoustic phonons. An extended object is defined as a classically behaving macroscopic object created through the boson condensation of phonons. An explicit microscopic derivation of the theory of extended objects in crystals is given. Extended objects can appear in crystals both with and without topological singularities. A general method for constructing extended objects with topological singularities is indicated. As examples, dislocations, grain boundaries, and point defects are studied in detail. Based on a new theory of the boundary surface, a novel derivation of surface waves is presented. Finally, further problems of the theory are discussed. Throughout the analysis, the boson transformation method is extensively used. © 1979.