Intrinsic momentum in Poincare gauge theory

TL;DR

This paper investigates the coupling of translational gauge fields to fermions within Poincare gauge theory, revealing that fermions do not carry intrinsic momentum due to inconsistencies in the assumed full Poincare representation.

Contribution

It demonstrates that assuming fermions carry a full Poincare representation leads to inconsistencies, showing translational fields do not minimally couple to fermions in this framework.

Findings

Fermions do not possess intrinsic momentum.

Translational gauge fields do not minimally couple to fermions.

Inconsistencies arise from assuming full Poincare representation for spinors.

Abstract

While it is generally accepted, in the framework of Poincare gauge theory, that the Lorentz connection couples minimally to spinor fields, there is no general agreement on the coupling of the translational gauge field to fermions. We will show that the assumption that spinors carry a full Poincare representation leads to inconsistencies, whose origins will be traced back by considering the Poincare group both as the contraction of the de Sitter group, and as a subgroup of the conformal group. As a result, the translational fields do not minimally couple to fermions, and consequently, fermions do not possess an intrinsic momentum.