Nontrivial vacuum solutions in flavor mixing and critical phenomena

The structure of the vacuum state plays profound role§in particle physics, being responsible for such§exciting phenomena as symmetry breaking,§Higgs-mediated mass generation, and many others.§Solutions for the nontrivial vacuum structure are§also important in flavor mixing, such as in the§mixing of neutrinos, and critical phenomena in§Quantum Field Theories - some of the most sensitive§tools available today to probe the physics beyond the§Standard Model. Using the method of§Bogolyubov-Valatin canonical transformation, we show§here how the exact structure of the vacuum state in§the quantum field theory of flavor mixing is derived,§which turns out to be a state unitary inequivalent to§the free-particle vacuum of the perturbation theory,§and develop the complete formulation of the flavor§mixing theory including the exact field-theoretic§mixing formulas and corrections to the charge§oscillations. We furthermore show how unitary§inequivalence may play the decisive role in the§radical degrees-of-freedom rearrangement during§phase transitions, likely to be responsible§for the phenomena such as quark-hadron duality and§the generation of constituent quark mass in Quantum§Chromodynamics.