The Quantum Theory of the Lorentzian Fermionic Differential Forms

TL;DR

This paper develops a quantum theory for Lorentzian fermionic differential forms and bi-spinor fields, introducing new mass terms and classifying solutions by a novel scalar spin quantum number, expanding the understanding of fermionic gauge theories.

Contribution

It presents a detailed canonical quantization of bi-spinor gauge theory, derives Feynman rules, and introduces the concept of scalar spin, a new quantum number in fermionic gauge theories.

Findings

Classified solutions by scalar spin quantum number.

Derived all possible mass terms for massive fermions.

Connected Lorentz spin of bi-spinors with scalar spin of constituents.

Abstract

We consider the quantum theory of the Lorentzian fermionic differential forms and the corresponding bi-spinor quantum fields, which are the expansion coefficients of the forms in the bi-spinor basis of Becher and Joos [7]. The canonical quantization procedure for the bi-spinor gauge theory in terms of its Dirac spinor constituents is described in detail and the corresponding Feynman rules are derived. We also derive all possible mass terms for massive fermions in the bi-spinor gauge theory. The solutions are classified by a scalar spin quantum number, a number that has no analog in the standard gauge theory and in the SM. The possible mass terms correspond to combinations of scalar spin zero singlets and scalar spin one-half doublets in the generation space. A description of the connection between Lorentz spin of bi-spinors and scalar spin of bi-spinor constituents is given.