Bosonized supersymmetry from the Majorana-Dirac-Staunton theory and massive higher-spin fields

TL;DR

This paper develops a covariant vector equation framework unifying spin 0 and 1/2 particles, extends it to massive higher-spin fields, and realizes space-time supersymmetry in a bosonized form with a nonlinear superalgebra.

Contribution

It introduces a novel covariant set of equations unifying spins and generalizes to a supersymmetric higher-spin theory using the Majorana equation.

Findings

Realizes space-time supersymmetry in a bosonized form.

Constructs a nonlinear superalgebra that reduces to super-Poincare algebra at large spin.

Describes a supermultiplet with different degrees of freedom in bosonic and fermionic sectors.

Abstract

We propose a (3+1)D linear set of covariant vector equations, which unify the spin 0 ``new Dirac equation'' with its spin 1/2 counterpart, proposed by Staunton. Our equations describe a spin (0,1/2) supermultiplet with different numbers of degrees of freedom in the bosonic and fermionic sectors. The translation-invariant spin deegres of freedom are carried by two copies of the Heisenberg algebra. This allows us to realize space-time supersymmetry in a bosonized form. The grading structure is provided by an internal reflection operator. Then the construction is generalized by means of the Majorana equation to a supersymmetric theory of massive higher-spin particles. The resulting theory is characterized by a nonlinear symmetry superalgebra, that, in the large-spin limit, reduces to the super-Poincare algebra with or without tensorial central charge.