Group theoretical derivation of consistent massless particle theories

TL;DR

This paper derives new classes of consistent massless particle theories using group theory and relativistic invariance, challenging previous assumptions about space inversion and time reversal operators.

Contribution

It introduces a deductive group-theoretical framework for massless particles, identifying theories consistent with invariance principles that were previously overlooked.

Findings

New classes of massless theories explicitly derived.

Constraints from invariance principle clarified and previously ignored.

Enhanced understanding of localizability for massless systems.

Abstract

Current theories of massless free particle assume {\sl unitary} space inversion and {\sl anti-unitary} time reversal operators. In so doing robust classes of possible theories are discarded. In the present work theories of massless systems are derived through a strictly deductive development from the principle of relativistic invariance, so that a kind of space inversion or time reversal operator is ruled out only if it causes inconsistencies. As results, new classes of consistent theories for massless isolated systems are explicitly determined. On the other hand, the approach determines definite constraints implied by the invariance principle; they were ignored by some past investigations that, as a consequence, turn out to be not consistent with the invariance principle. Also the problem of the localizability for massless systems is reconsidered within the new theoretical framework, obtaining a generalization and a deeper detailing of previous results.