From isospin generators to BRST quantization of higher spin massless fields

TL;DR

This paper establishes an equivalence between isospin generator algebra and the Virasoro algebra, leading to a BRST quantization approach for massless higher spin fields, revealing connections to gauge theories of various fundamental fields.

Contribution

It introduces a novel matrix product to relate isospin and Virasoro algebras, enabling BRST quantization of higher spin fields within a unified framework.

Findings

Derived a gauge theory for infinite non-interacting massless particles of arbitrary spin.

Reproduced gauge transformations for Maxwell, gravitational, and axion fields.

Established an algebraic equivalence linking particle physics and string theory structures.

Abstract

Motivated by construction of isospin generators in particle physics (built form the SU(2) algebra), we find an equivalence between the algebra of these generators and those of the Virasoro algebra. The form of the starting generators is fixed and in order to obtain a full equivalence we introduce a new matrix product. The Cartan structure of the starting algebra is reproduced for the Virasoro-like case and a natural BRST quantization as in String Field Theory is ``induced'' in the Fock space of the creation/annihilation operators. Following this procedure, we find a rather trivial Lie algebra form which we obtain a gauge theory of an infinity on non-interacting massless particles of arbitrary integer spin and symmetry. Among others we find the free Maxwell field, the free (linearized) gravitational field and also the axion field with their appropriate gauge transformations.