Quantum Roots in Geometry: II

TL;DR

This paper reviews how non-symmetric geometries inherently contain quantum features, highlighting the role of torsion in space-time and introducing a new geometric framework, PAP geometry, for developing quantum-compatible field theories.

Contribution

It introduces Parameterized Absolute Parallelism (PAP) geometry, a new framework that generalizes Riemannian and AP geometries to incorporate quantum features through torsion.

Findings

Torsion in space-time interacts with particle spin and charge.

Non-symmetric geometries exhibit built-in quantum features.

PAP geometry unifies Riemannian and AP geometries with quantum properties.

Abstract

The present work is a review of a series of papers, published in the last ten years, comprising an attempt to find a suitable avenue from geometry to quantum. It shows clearly that, any non-symmetric geometry admits some built-in quantum features. These features disappear completely once the geometry becomes symmetric (torsion-less). It is shown that, torsion of space-time plays an important role in both geometry and physics. It interacts with the spin of the moving particle and with its charge. The first interaction, {\bf{Spin-Torsion Interaction}}, has been used to overcome the discrepancy in the results of the COW-experiment. The second interaction, {\bf{Charge-Torsion Interaction}}, is similar to the Aharonov-Bohm effect. As a byproduct, a new version of Absolute Parallelism (AP) geometry, the Parameterized Absolute Parallelism (PAP) geometry, has been established and developed. This version can be used to construct field theories that admit some quantum features. Riemannian geometry and conventional AP-geometry are special cases of PAP-geometry.