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Majorana mass term and CAR algebra of creation and annihilation operators of Dirac and Majorana spinors
1  Saint Petersburg State University
Academic Editor: Gerald Cleaver

Published: 15 February 2023 by MDPI in 2nd Electronic Conference on Universe session Field Theory

We have proved that, under the standard charge conjugation approach, the Majorana mass term must vanish not only in the so called c-theory, which was known, but also in the q-theory (the theory of second quantization). In this case, the possible influence of the phase factor during charge conjugation is taken into account. It turned out that it does not affect the result.
We have derived formulas for Majorana spinor field operators without any assumptions about second quantization procedure. We have proved that the Hamiltonian of the Majorana spinor at zero momentum is zero.
The fact that the Majorana mass term and the Hamiltonian of the Majorana spinor vanish at zero momentum requires a revision of ideas about the generation of neutrino mass using the seesaw and other mechanisms.

Keywords: Clifford algebra; CAR algebra; Lie groups; spinors; Majorana spinors; Majorana fermion; gauge transformations; second quantization