A New Form of the Baryteron Equation and Some Related Questions

Abstract

IT is known that the 2-component spinors introduced by Van der Waerden must be completed to 4-component quantities if linear transformation of their components by the complete Lorentz group including reflections is required. These quantities, often called ‘Dirac wave-functions’, will be called here ‘four-spinors’ or ‘undors* of the first rank’. Defining the reflection in the right way¹, it is possible to join to every four-spinor ψ another four-spinor² ψ^£, the components of which are linear combinations of those of ψ^*. This ψ^£ is called the charge-conjugated³ of ψ. For if ψ is a solution of the Dirac equation for a positive particle, then ψ^£ is a solution of the Dirac equation for a negative paricle: vice versa ( ψ^££ = ψ). Four-spinors, which are equal to their own charge-conjugated, we may call neutrinors. These quantities, which are equivalent to a two-spinor together with its complex conjugated, are not only useful in the so-called neutrino theory of light, but also Majorana's theory of neutrons⁴ may be summarized by stating that the quantized fourspinor of a neutral particle is neutrinor.