On Geometric Structure of Point Particles

TL;DR

This paper introduces a geometric model of point particles using a helical internal space structure, linking plasma physics analogies to particle properties and suggesting implications for fundamental physics and higher-dimensional frameworks.

Contribution

It develops a novel geometric approach to point particles based on helical fields and plasma analogies, connecting internal space structures to particle properties and symmetries.

Findings

Helical internal fields can model intrinsic particle properties.

Rotational eigenvalue equations relate to coordinate-rotors and charge normalization.

Chiral asymmetry in eigenflows may reflect electroweak symmetry breaking.

Abstract

I propose, as geometric structure in an internal space, a helical field that is responsible for intrinsic properties of point particles, particularly, electron. For the novel theoretical development, plasma astrophysical analogy is made extensively. Transition between our conventional space and the infinitesimal space is considered in an operational manner. It is shown that rotational eigenvalue equation satisfied by the vector field equivalent to Gromeka-Beltrami flow provides a coordinate-rotor that captures complex orthogonality between the internal coordinate space and isotopic, angular momentum space. Self-consistent normalization of rotational coordinate owing to the rotor is compared to renormalization of electric charge. It is also found that chiral asymmetry of the helical eigenflows can be reflected in electroweak symmetry breaking. The theoretical prototype suggests possible geometrical features of a fundamental framework ruling matters and forces with higher dimensions.