Abstract
Simultaneous treatment of neutrino oscillations and collisions in astrophysical environments requires the use of (quantum) kinetic equations. Despite major advances in the field of quantum kinetics, the structure of the kinetic equations and their consistency with the uncertainty principle are still debated. The goals of the present work are threefold. First, it clarifies the structure of the Liouville term in the presence of mixing. Second, we derive evolution equation for neutrinos propagating in vacuum or matter from the Schrödinger equation and show that in the relativistic limit its form matches the form of the (collisionless part of the) kinetic equation derived by Sigl and Raffelt. Third, by constructing solutions of the evolution equation from the known solutions of the Schrödinger equation, we show that the former also admits solutions consistent with the uncertainty principle and accounts for neutrino wave packet separation. The obtained results speak in favor of a (quantum) kinetic approach to the analysis of neutrino propagation in exploding supernovae where neutrino oscillations and collisions, as well as the effect of wave packet separation, might be equally important.
Highlights
On the other hand, neutrino collisions with particles of the ambient medium can play a dominant role in certain phases of supernovae evolution [9]
We derive evolution equation for neutrinos propagating in vacuum or matter from the Schrodinger equation and show that in the relativistic limit its form matches the form of the kinetic equation derived by Sigl and Raffelt
Because particle number is conserved in quantum mechanics, description of neutrino production and absorption processes typically relies on the Boltzmann kinetic equation for the neutrino occupation numbers
Summary
We consider neutrino propagation in vacuum and establish a connection between three technically different approaches to description of flavor neutrino oscillations. In subsection 2.1 we briefly review the quantum-mechanical approach operating with the neutrino wave function ψi(t, x) or density matrix ρij(t, x). In subsection 2.2 we derive evolution equation for the two-point correlatorij(t, x, ǫ, p) from the Schrodinger equation. Its form matches (the vacuum limit of) the quantum kinetic equation. In subsection 2.3 we derive evolution equation for the Wigner functionij(t, x, p) from the evolution for the two-point correlator using on-shell approximation. In the physically relevant relativistic limit its form matches (the vacuum limit of) the kinetic equation of Sigl and Raffelt
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