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

We investigate Leggett-Garg inequalities for neutrino oscillations in the quantum field theoretical setting. We derive an exact flavor-mass uncertainty relation and prove that this uncertainty product yields an upper bound to the violation of the inequalities. The relation between temporal nonclassicality and quantum uncertainty real-izes the Luders upper bound to the violation of the Leggett-Garg inequalities in quantum field theory, analogous to the Tsirelson upper bound to the violation of the Bell inequalities. By studying the problem both in the exact field-theoretical setting and in the limiting quantum mechanical approximation, we show that on average the inequalities are violated more often and more strongly in quantum field theory than in quantum mechanics.