Spin 1/2 and Invariant Coefficients II. Massless

TL;DR

This paper explores how massless spin 1/2 fields can be described using invariant coefficients, deriving wave equations and Maxwell-like relations without assuming traditional properties, suggesting a universal charge for such particles.

Contribution

It extends the invariant coefficient hypothesis to massless spin 1/2 fields, deriving wave equations and electromagnetic relations without prior assumptions, unifying massive and massless cases.

Findings

Derives Weyl and Weyl-like wave equations for massless fields.

Shows Maxwell equations are satisfied without assuming them.

Suggests a universal electromagnetic charge for spin 1/2 particles.

Abstract

A `covariant' field that transforms like a relativistic field operator is required to be a linear combination of `canonical' fields that transform like annihilation and creation operators and with invariant coefficients. The Invariant Coefficient Hypothesis contends that this familiar construction by itself yields useful results. Thus, just the transformation properties are considered here, not the specific properties of annihilation or creation operators. The results include Weyl wave equations for some massless fields and, for other fields, Weyl-like noncovariant wave equations that are allowed here because no assumptions are made to exclude them. The hypothesis produces wave equations for translation-matrix-invariant fields while translation-matrix-dependent coefficient functions have currents that are the vector potentials of the coefficient functions of those translation-matrix-invariant fields. The statement is proven by showing that Maxwell equations are satisfied, though in keeping with the hypothesis they are not assumed to hold. The underlying mechanism is the same for the massless class here as it is for the massive class in a previous paper, suggesting that spin 1/2 particles may have a universal electromagnetic-type charge whether they are massive or massless. Keywords: Relativistic quantum fields; neutrino; Poincare transformations