"Minimal geometric data" approach to Dirac algebra, spinor groups and field theories

TL;DR

This paper presents a geometric approach to spinor theory and field theories using intrinsic 2-spinor geometry, deriving background structures from a single vector bundle without additional assumptions.

Contribution

It introduces a minimal geometric data framework for spinor geometry and explores Dirac algebra and 4-spinor groups from a novel perspective.

Findings

Natural emergence of background structures from a single geometric datum

Reinterpretation of Dirac algebra in terms of two spinors

Analysis of particle momenta using 2-spinor formalism

Abstract

The three first sections contain an updated, not-so-short account of a partly original approach to spinor geometry and field theories introduced by Jadczyk and myself; it is based on an intrisic treatment of 2-spinor geometry in which the needed background structures do not need to be assumed, but rather arise naturally from a unique geometric datum: a vector bundle with complex 2-dimensional fibres over a real 4-dimensional manifold. The two following sections deal with Dirac algebra and 4-spinor groups in terms of two spinors, showing various aspects of spinor geometry from a different perspective. The last section examines particle momenta in 2-spinor terms and the bundle structure of 4-spinor space over momentum space.