Lie sphere geometry in nuclear scattering processes

TL;DR

This paper explores how Lie sphere geometry extends M"obius geometry and offers a natural framework for Clifford algebras, potentially aiding in the geometrization of internal particle symmetries in nuclear scattering.

Contribution

It introduces the application of Lie sphere geometry to higher-dimensional space-time models, enhancing the Clifford algebra structure for particle symmetry analysis.

Findings

Lie sphere geometry provides a more natural Clifford algebra structure.

Potential for geometrizing internal particle symmetries.

A simple model includes electromagnetic and isospin interactions.

Abstract

The Lie sphere geometry is a natural extension of the M\"obius geometry, where the latter is very important in string theory and the AdS/CFT correspondence. The extension to Lie sphere geometry is applied in the following to a sequence of M\"obius geometries, which has been investigated recently in a bicomplex matrix representation. When higher dimensional space-time geometries are invoked by inverse projections starting from an originating point geometry, the Lie sphere scheme provides a more natural structure of the involved Clifford algebras compared to the previous representation. The spin structures resulting from the generated Clifford algebras can potentially be used for the geometrization of internal particle symmetries. A simple model, which includes the electromagnetic spin, the weak isospin, and the hadronic isospin, is suggested for further verification.