3+1D Massless Weyl spinors from bosonic scalar-tensor duality

TL;DR

This paper demonstrates how a 3+1D bosonic scalar-tensor duality can be used to explicitly construct massless Weyl spinors, revealing a fermionization process rooted in topological and boundary considerations.

Contribution

It provides a novel explicit construction of 3+1D Weyl spinors from bosonic fields using scalar-tensor duality and tomographic representation, linking topological theories to fermionic particles.

Findings

Constructed fermionic operators satisfying anticommutation relations

Demonstrated these operators obey the massless Dirac equation

Expressed charge density in terms of bosonic degrees of freedom

Abstract

We consider the fermionization of a bosonic free theory characterized by the 3+1D scalar - tensor duality. This duality can be interpreted as the dimensional reduction, via a planar boundary, of the 4+1D topological BF theory. In this model, adopting the Sommerfield tomographic representation of quantized bosonic fields, we explicitly build a fermionic operator and its associated Klein factor such that it satisfies the correct anticommutation relations. Interestingly, we demonstrate that this operator satisfies the massless Dirac equation and that it can be identified with a 3+1D Weyl spinor. Finally, as an explicit example, we write the integrated charge density in terms of the tomographic transformed bosonic degrees of freedom.