Bosonization in four dimensions: The smooth way

TL;DR

This paper explores a smooth bosonization method in four dimensions, transforming fermionic theories into bosonic ones using chiral phases, and discusses the resulting nonlinear field theory with potential soliton-fermion correspondence.

Contribution

It introduces a novel smooth bosonization scheme in four dimensions based on chiral phases, providing an exact reformulation of fermionic theories with insights into soliton-fermion duality.

Findings

Exact bosonization includes fermions, bosons, and ghosts

The bosonic action is derived from the Jacobian of variable change

The resulting nonlinear theory may support topological solitons

Abstract

I investigate bosonization in four dimensions, using the smooth bosonization scheme. I argue that generalized chiral ``phases'' of the fermion field corresponding to chiral phase rotations and ``chiral Poincare transformations'' are the appropriate degrees of freedom for bosonization. Smooth bosonization is then applied to an Abelian fermion coupled to an external vector. The result is an exact rewriting of the theory, including the fermion, the bosonic fields, and ghosts. Exact bosonization is therefore not achieved since the fermion and the ghosts are not completely eliminated. The action for the bosons is given by the Jacobian of a change of variables in the path integral, and I calculate parts of this. The action describes a nonlinear field theory, and thus static, topologically stable solitons may exist in the bosonic sector of the theory, which become the fermions of the original theory after quantization.