Note on Dirac--K\"ahler massless fields

TL;DR

This paper analyzes the properties of massless Dirac–Kähler fields, deriving their energy-momentum tensors, examining symmetry breaking, and establishing a quantization framework with propagators.

Contribution

It provides explicit forms of energy-momentum tensors, identifies non-conservation of dilatation currents, and introduces a new conserved dilatation current for massless Dirac–Kähler fields.

Findings

Energy-momentum tensors have non-zero traces.

Dilatation currents are not conserved, indicating broken conformal symmetry.

A quantization scheme with propagator expressions is developed.

Abstract

We obtain the canonical and symmetrical Belinfante energy-momentum tensors of Dirac--K\"{a}hler's fields. It is shown that the traces of the energy-momentum tensors are not equal to zero. We find the canonical and Belinfante dilatation currents which are not conserved, but a new conserved dilatation current is obtained. It is pointed out that the conformal symmetry is broken. The canonical quantization is performed and the propagator of the massless fields in the first-order formalism is found.