Bosonization of Weyl Fermions and Free Electrons

TL;DR

This paper generalizes bosonization to 3+1 dimensions, unifying the description of electrons and Weyl fermions via the Kalb-Ramond field, and explains observed magneto-conductance behaviors.

Contribution

It presents the first complete bosonization of 3+1D fermions, linking electrons and Weyl fermions through a common bosonic framework.

Findings

Electrons and Weyl fermions can be described by the same bosonic field.

The bosonized form explains angle-dependent magneto-conductance.

The method extends bosonization to higher-dimensional spacetime.

Abstract

The electron, discovered by Thomson by the end of the nineteenth century, was the first experimentally observed particle. The Weyl fermion, though theoretically predicted since a long time, was observed in a condensed matter environment in an experiment reported only a few weeks ago. Is there any linking thread connecting the first and the last observed fermion (quasi)particles? The answer is positive. By generalizing the method known as bosonization, the first time in its full complete form, for a spacetime with 3+1 dimensions, we are able to show that both electrons and Weyl fermions can be expressed in terms of the same boson field, namely the Kalb-Ramond anti-symmetric tensor gauge field. The bosonized form of the Weyl chiral currents lead to the angle-dependent magneto-conductance behavior observed in these systems.