Theory of spin one half bosons

TL;DR

This paper explores a novel quantum field for spin one half bosons, constructed from the square root of the identity matrix, revealing unique degrees of freedom and potential implications for cosmological neutrino models.

Contribution

It introduces a new mass dimension one bosonic field with properties distinct from known bosons, linked to spin one half fermions and parity violation.

Findings

Constructed a new bosonic quantum field with spin one half.

Identified maximum parity violation arising from locality constraints.

Linked the new bosons to cosmological neutrino theories.

Abstract

These are notes on the square root of $4\times4$ identity matrix and associated quantum fields of spin one half. The method is illustrated by constructing a new mass dimension one bosonic field. The locality constraint for the field leads naturally to maximum parity violation. The degrees of freedom carried by the new bosons are different from any massive boson previously encountered and coincide with those carried by spin one half fermions. We thus provide a quantum field suspected to exist by Dolgov and Smirnov in the context of cosmological neutrinos.