Abstract
A variation of the theory of fermions is proposed in which the fermions are described by two-component spinors obeying a relativistic equation of the second order. In order to make the probability density of the spin-1/2 particles positive definite, the rule is established that complex conjugation of functions and Hermitian conjugation of operators are accompanied by the operation of spatial reflection. A one-particle theory in Hamiltonian form, a Lagrangian formalism for a free two-component field, and the second quantization of the theory are derived. For calculations in quantum electrodynamics a Hamiltonian is proposed similar to the interaction Hamiltonian of spinless particles with the electromagnetic field but containing a spin-dependent part.
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