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Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU)

Quantum field theory at finite time and neutrino oscillations

Massimo Blasone A, Francesco Giacosa, L. A. Smaldone, Giorgio Torrieri

Published Jul 31, 2024• 1 citation

Abstract

We discuss the role of finite time and energy uncertainty in the quantum field theory description of neutrino oscillations. In order to to achieve this goal, we review the flavor Fock-space approach and the time-energy uncertainty relation in the Mandelstam--Tamm form, expressed as a flavor-energy uncertainty relation. Such relation, together with the inequivalence of mass and flavor neutrinos Fock spaces, puts a lower bound on neutrino energy uncertainty. Similar considerations can be derived by a perturbative computation of flavor transitions, which employs the Dirac picture to compute flavor transition probability. Remarkably, both flavor Fock space and interaction picture approach lead to the same oscillation probability, within the approximation adopted in the perturbative calculation.

DOI: 10.22323/1.463.0098

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Neutrino oscillations is a phenomenon which is characterized by a finite oscillation time (length). For such phenomena time-energy uncertainty relation is valid. This means that energy uncertainty is needed for oscillations to occur. We consider neutrino oscillations from this point of view. We demonstrate that for mixed neutrino states, which describe flavor neutrinos

ν_{e}

,

ν_μ

and

ν_τ

, translational invariance does not take place.

Neutrino oscillations is a phenomenon which is characterized by a finite oscillation time (length). For such phenomena time-energy uncertainty relation is valid. This means that energy uncertainty is needed for oscillations to occur. We consider neutrino oscillations from this point of view. We demonstrate that for mixed neutrino states, which describe flavor neutrinos

\\nu_{e}

,

\\nu_{\\mu}

and

\\nu_{\\tau}

, translational invariance does not take place.

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 realizes the L\"uders 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.