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.

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