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

Understand

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.