From Pure Spinors to Quantum Physics and to Some Classical Field Equations Like Maxwell's and Gravitational

TL;DR

This paper explores a mathematical framework linking pure spinors to quantum mechanics and classical field equations, proposing new tensor structures for gravity and electromagnetism within the spinor formalism.

Contribution

It introduces a symmetric tensor quadrilinear in simple spinors as a candidate for the gravitational field, extending previous work on spinor-based quantum mechanics.

Findings

Proposes a spinor-based tensor approach to gravity.

Derives Maxwell's equations from bilinear spinor constructs.

Suggests potential solutions to Standard Model problems.

Abstract

In a previous paper [1] we proposed a purely mathematical way to quantum mechanics based on Cartan's simple spinors in their most elementary form of 2 component spinors. Here we proceed along that path proposing, this time, a symmetric tensor, quadrilinear in simple spinors, as a candidate for the symmetric tensor of general relativity. This is allowed now, after the discovery of the electro-weak model and its introduction in the Standard Model with SU(2)_L. The procedure resembles closely that in which one builds bilinearly from simple spinors an antisymmetric "electromagnetic tensor", from which easily descend Maxwell's equations and the photon can be seen as a bilinear combination of neutrinos. Here Lorentzian spaces result compact, building up spheres, where hopefully some of the problems of the Standard Model could be solved as pointed out in the conclusions.