Bosonization of Fermionic Fields and Fermionization of Bosonic Fields

TL;DR

This paper demonstrates the mathematical equivalence between fermionic and bosonic fields using Clifford bundle formalism, providing a rigorous foundation for bosonization and fermionization in quantum field theory.

Contribution

It introduces a formalism that explicitly relates fermionic and bosonic fields via Clifford bundles, extending the understanding of their equivalence.

Findings

Fermionic fields are equivalent to classes of bosonic fields.

Bosonic fields are equivalent to classes of fermionic fields.

The formalism clarifies the mathematical structure of bosonization and fermionization.

Abstract

In this paper using the Clifford and spin-Clifford bundles formalism we show how Weyl and Dirac equations formulated in the spin-Clifford bundle may be written in an equivalent form as generalized Maxwell like form formulated in the Clifford bundle. Moreover, we show how Maxwell equation formulated in the Clifford bundle formalism can be written as an equivalent equation for a spinor field in the spin-Cillford bundle. Investigating the details of such equivalences this exercise shows explicitly that a fermionic field is equivalent (in a precise sense) to an equivalence class of well defined boson fields and that a bosonic field is equivalent to a well defined equivalence class of fermionic fields These equivalences may be called the bosonization of fermionic fields and the fermionization of bosonic fields.