Applications of canonical transformations and nontrivial vacuum solutions to flavor mixing and critical phenomena in quantum field theory

Abstract

This dissertation deals with recent applications of Bogoliubov transformation to the phenomenology of quantum flavor mixing and to the study of critical phenomena in quantum field theories. The dissertation contains a brief review of canonical transformations, with a special emphasis on linear quantum canonical transformation (Bogoliubov transformation), as they appear in classical and quantum physics and their applications in superfluidity and low energy quantum chromodynamics (QCD). Then, the general quantum field theory of flavor mixing is introduced with Bogoliubov transformation, space-time conversion is considered and effects for phenomenology of flavor oscillations in time and space is presented. Furthermore, the Oscillator Representation Method, relevant to analysis of degrees-of-freedom rearrangement during phase transitions, is fully reviewed and illustrated. Nontrivial vacuum condensation, dynamical mass generation and duality are all incorporated as parts of this approach. Specific applications to phase transition in nonlinear sigma model and phi∧4 scalar quantum field theory are presented and possibilities for further method improvement are considered. A new independent variational approach, method of Symmetric Decomposition Problem, is also fully introduced, illustrated and applied to the analysis of the ground state in a variant of nonlinear sigma model. In this method, the structure of the Fock space in terms of the expectation values of given quantum operators is found and used to reformulate and exactly solve variational problem for the ground state of the above mentioned quantum field theory.