Canonical quantization of a massive Weyl field

Abstract

We construct a consistent theory of a quantum massive Weyl field. We start with the formulation of the classical field theory approach for the description of massive Weyl fields. It is demonstrated that the standard Lagrange formalism cannot be applied for the studies of massive first-quantized Weyl spinors. Nevertheless we show that the classical field theory description of massive Weyl fields can be implemented in frames of the Hamilton formalism or using the extended Lagrange formalism. Then we carry out a canonical quantization of the system. The independent ways for the quantization of a massive Weyl field are discussed. We also compare our results with the previous approaches for the treatment of massive Weyl spinors. Finally the new interpretation of the Majorana condition is proposed.

6 pages in Revtex 4.1, two columns, no figures; paper is significantly revised, the discussion of the extended Lagrange formalism is included, several new references are added; accepted for publication in Foundation of Physics

References in corpus (6)

• Observation of electron-antineutrino disappearance at Daya Bay
• Indication for the disappearance of reactor electron antineutrinos in the Double Chooz experiment
• Search for Neutrinoless Double-Beta Decay in ${}^{136}$Xe with EXO-200
• 130Te Neutrinoless Double-Beta Decay with CUORICINO
• Field theory description of neutrino oscillations
• Oscillations of Dirac and Majorana neutrinos in matter and a magnetic field

Cited by in corpus (5)

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• 'Majorana mass' fermions as untrue Majorana particles, rather endowed with pseudoscalar-type charges than genuinely neutral
• Meronic Einstein-Yang-Mills black hole in 5D and gravitational spin from isospin effect
• Quantization of massive Weyl fields in vacuum
• Massive Majorana neutrinos in matter and a magnetic field