Spinors in Quantum Geometrical Theory

TL;DR

This paper explores integrating spinors into a five-dimensional quantum-geometrical framework, aiming to deepen the understanding of fundamental physics and naturally generate spinor structures within the theory.

Contribution

It proposes a novel approach to include spinors in quantum geometry, extending existing theories and seeking a natural emergence of spinor structures from geometric principles.

Findings

Reformulation of classical physics as quantum geometry

Resolution of wave-particle duality enigma

Initial steps towards deriving spinors from geometry

Abstract

Spinors have played an essential but enigmatic role in modern physics since their discovery. Now that quantum-gravitational theories have started to become available, the inclusion of a description of spin in the development is natural and may bring about a profound understanding of the mathematical structure of fundamental physics. A program to attempt this is laid out here. Concepts from a known quantum-geometrical theory are reviewed: (1) Classical physics is replaced by a suitable geometry as a fundamental starting point for quantum mechanics. (2) In this context, a resolution is found for the enigma of wave-particle duality. (3) It is shown how to couple the quantum density to the geometrical density. (4) The mechanical gauge is introduced to allow dimensional reduction. (5) Absolute geometrical equivalence is enforced. The concordant five-dimensional quantum-geometrical theory is summarized to provide an orderly basis for the introduction of spinors. It is supposed that the Pauli--Dirac theory is adaptable. A search is begun for a description that will generate spinors as a natural tangent space. Interactions other than gravity and electrodynamics should then appear intrinsically. These are conjectured to be weak effects for electrons.