The Quantum Theory of the Lorentzian Fermionic Differential Forms

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.