3+1D Massless Weyl Spinors from Bosonic Scalar-Tensor Duality

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.