Leggett-Garg inequalities in the quantum field theory of neutrino oscillations

We investigate Leggett-Garg temporal inequalities in flavor-mixing processes. We derive an exact flavor-mass uncertainty relation and we prove that this gives an upper bound to the violation of the inequalities. This finding relates temporal nonclassicality to quantum uncertainty and provides a time analog of the Tsirelson upper bound to the violation of the spatial Bell inequalities. By studying the problem both in the exact field-theoretical setting and in the limiting quantum mechanical approximation, we show that the inequalities are violated more strongly in quantum field theory than in quantum mechanics.