The 2(2S+1)- Formalism and Its Connection with Other Descriptions

TL;DR

This paper explores the Joos-Weinberg 2(2S+1)- theory for massless particles, deriving invariants, establishing equivalences with other formulations, and proposing a new interpretation of the Weinberg field function, with implications for high-spin particles.

Contribution

It introduces a new gauge invariance in the Joos-Weinberg theory and offers a novel interpretation of the Weinberg field function for massless particles.

Findings

Derived dynamical invariants from the Lagrangian density.

Established equivalence between the scalar Lagrangian and Hayashi's free massless field.

Proposed a new interpretation of the Weinberg field function.

Abstract

In the framework of the Joos-Weinberg 2(2S+1)- theory for massless particles, the dynamical invariants have been derived from the Lagrangian density which is considered to be a 4- vector. A la Majorana interpretation of the 6- component "spinors", the field operators of S=1 particles, as the left- and right-circularly polarized radiation, leads us to the conserved quantities which are analogous to those obtained by Lipkin and Sudbery. The scalar Lagrangian of the Joos-Weinberg theory is shown to be equivalent to the Lagrangian of a free massless field, introduced by Hayashi. As a consequence of a new "gauge" invariance this skew-symmetric field describes physical particles with the longitudinal components only. The interaction of the spinor field with the Weinberg's 2(2S+1)- component massless field is considered. New interpretation of the Weinberg field function is proposed. KEYWORDS: quantum electrodynamics, Lorentz group representation, high-spin particles, bivector, electromagnetic field potential. PACS: 03.50.De, 11.10.Ef, 11.10.Qr, 11.17+y, 11.30.Cp