Tachyons with any Spin

TL;DR

This paper extends a method for handling spin 1/2 tachyons to tachyons of any spin, developing a Dirac-like equation with multiple mass eigenvalues that can model neutrino mass spectra.

Contribution

It introduces a generalized approach for tachyons of any spin, including a Dirac-like equation and a basis for SU(3) Lie algebra, expanding the theoretical framework for tachyonic particles.

Findings

Developed a Dirac-like equation for tachyons of any half-integer spin.

Found a basis for SU(3) Lie algebra relevant to tachyonic states.

Model can be tuned to match neutrino mass data.

Abstract

In earlier work we showed how to handle the Group Theoretical issue of the Little Group for spin 1/2 tachyons by introducing a special metric in the Hilbert space of one-particle states. Here that technique is extended to tachyons of any spin. Examining the bi-linear algebra of the generating matrices for spin 5/2, we find a complete basis for the Gell-Mann matrices that form the Lie algebra for SU(3). A Dirac-like equation is developed for tachyons of any integer-plus-one-half spin; and it shows multiple distinct mass eigenvalues. The primary model shows a mass spectrum (in the case of j = 5/2) that roughly mimics the known data on masses of the three neutrinos; the model can be tweaked to fit that experimental data precisely.