Applications of effective field theory to condensed matter

Effective field theory is a very powerful tool in quantum field theory, and in particular gives a very efficient method to predict results for experiments. It also allows one to show in a fairly convincing way whether a simplified microscopic model is the correct first step in a consistent approximation scheme. Yet, its application to condensed matter physics has not been widely appreciated. Much work remains to be done. We shall apply the effective field theory technique to a variety of condensed matter systems such as Bose-Einstein condensates, superfluids, high $Tc$ superconductors, strongly correlated electrons, etc. The main aim of this thesis is to show that effective field theories for a class of such systems can be derived directly from the spontaneous symmetry breakdown without relying on detailed microscopic models. The use of effective field theories allows us to show that many fundamental properties of these systems are in fact model-independent consequences of the spontaneous breakdown of symmetries. They are universal and robust. Our results are closely compared with existing experimental data, or are used to give new predictions, or both. In particular, the application of effective field theory to Bose-Einstein condensation has enabled us to resolve a puzzle—the damping of collective excitations discovered in the recent experiments of Bose-Einstein condensates.