Bosonization of free Weyl fermions

Abstract

We generalize the method of bosonization, in its complete form, to a spacetime with 3 + 1 dimensions, and apply it to free Weyl fermion fields, which thereby, can be expressed in terms of a boson field, namely the Kalb–Ramond anti-symmetric tensor gauge field. The result may have interesting consequences both in condensed matter and in particle physics. In the former, the bosonized form of the Weyl chiral currents provides a simple explanation for the angle-dependent magneto-conductance recently observed in materials known as Weyl semimetals. In the latter, conversely, since electrons can be thought of as a combination of left and right Weyl fermions, our result suggests the possibility of a unified description of the elementary particles, which undergo the fundamental interactions, with the mediators of such interactions, namely, the gauge fields. This would fulfill the pioneering attempt of Skyrme, to unify the particles with their interaction mediators (Skyrme 1962 Nucl. Phys. 31 556).