Flavor-energy uncertainty relations for neutrino oscillations in quantum field theory

Abstract

In the context of quantum field theory, we derive flavor-energy uncertainty relations for neutrino oscillations. By identifying the nonconserved flavor charges with the ``clock observables,'' we arrive at the Mandelstam-Tamm version of time-energy uncertainty relations. In the ultrarelativistic limit, these relations yield the well-known condition for neutrino oscillations. Ensuing nonrelativistic corrections to the latter are explicitly evaluated. The analogy among flavor states and unstable particles and a novel interpretation of our uncertainty relations, based on the unitary inequivalence of Fock spaces for flavor and massive neutrinos, are also discussed.