Dynamical Generation of Fermion Mixing
A careful non perturbative study of flavor mixing reveals an interesting
structure of the flavor vacuum. This is deeply related to the existence of
unitarily inequivalent representations of field algebra in Quantum Field
Theory. Far from being a mathematical curiosity, this study leads to
phenomenological corrections to the neutrino oscillations formula.
The particle-antiparticle condensate structure of the flavor vacuum
suggests the idea of fermion mixing as an emergent dynamical phenomenon.
We present some general ideas, in models presenting chiral symmetry,
showing how an anomalous vacuum condensation is required in order to
dynamically generate mixing. This can be achieved by studying the algebra
of charges and currents.
Then we show how these ideas apply in a simple, but instructive, toy model
a la Nambu--Jona Lasinio, looking at the vacuum structure thanks to the
formalism developed by Umezawa, Takahashi and Kamefuchi to study dynamical
symmetry breaking and mass generation.
Remark: I am lactose intolerant.