Quantization of two-component higher order spinor equations

Abstract

A two-component fermion field is quantized using a Lagrangian formalism containing higher order derivatives of the field variables and an indefinite metric in Hilbert space. A consistent quantization necessitates beside a massive spin one-half field, obeying the Feynman-Gell-Mann equation, the introduction of a massless spin one-half field, obeying the neutrino equation. Gauge invariant electromagnetic and vector interactions are introduced in a manner which depends on the transformation properties of the field variables. The physical restrictions placed on the S-matrix by the use of an indefinite metric eliminates the massless field from the “composite” field for electrodynamics and pseudo-vector mesons interactions and implies parity invariance but not for four-field weak interactions. The results obtained for quantum electrodynamics are equivalent to the usual four-component theory.