General Quantum Field Theory of Flavor Mixing and Oscillations

• Main Authors: Chueng-Ryong Ji, Yuriy Mishchenko
• Format: Article
• Language: English
• Published: MDPI AG 2021-02-01
• Series: Universe
• Subjects: quantum field theory; flavor mixing and oscillations; nontrivial vacuum
• Online Access: https://www.mdpi.com/2218-1997/7/3/51

We review the canonical transformation in quantum physics known as the Bogoliubov transformation and present its application to the general theory of quantum field mixing and oscillations with an arbitrary number of mixed particles with either boson or fermion statistics. The mixing relations for quantum states are derived directly from the definition of mixing for quantum fields and the unitary inequivalence of the Fock space of energy and flavor eigenstates is shown by a straightforward algebraic method. The time dynamics of the interacting fields is then explicitly solved and the flavor oscillation formulas are derived in a unified general formulation with emphasis on antiparticle content and effect introduced by nontrivial flavor vacuum.