Time evolution of the lepton numbers of Majorana neutrinos in the Schrodinger picture versus Heisenberg picture

Takuya MOROZUMI, Nicholas J. Benoit, Yuta Kawamura
2022 Proceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2021)   unpublished
In this paper, we study the time evolution of the expectation value of Majorana neutrino with the Schrödinger picture. The operators with the definite lepton number and operators with the definite mass are related to each other by a Bogolyubov transformation. Then the vacuum with the null lepton number is also related to the vacuum for the massive operator and it is written by the superposition of the vacuum for massive field and Majorana pairs condensed states. We choose the state with a
more » ... te lepton number = 1 and the momentum q ≠ 0 as an initial state. By writing the state in terms of the superposition of energy eigenstates, we are able to study the time evolution of the state in the Schrödinger picture. The expectation value of lepton number operator is computed and it reproduces the same result as that obtained in the corresponding Heisenberg operator.
doi:10.22323/1.406.0063 fatcat:24u52ijwkrb6dibzw6hxm6fo2e