We present a general theory of mixing for an arbitrary number of fields with integer or half-integer spin. The time dynamics of the interacting fields is solved and the Fock space for interacting fields is explicitly constructed. The unitary inequivalence of the Fock space of base (unmixed) eigenstates and the physical mixed eigenstates is shown by a straightforward algebraic method for any number of flavors in boson or fermion statistics. The oscillation formulas based on the nonperturbative vacuum are derived in a unified general formulation and then applied to both two- and three-flavor cases. Especially, the mixing of spin-1 (vector) mesons and the Cabibbo-Kobayashi-Maskawa mixing phenomena in the standard model are discussed, emphasizing the nonperturbative vacuum effect in quantum field theory.

• Received 12 December 2001

DOI:https://doi.org/10.1103/PhysRevD.65.096015