Pre-geometric structure of quantum and classical particles in terms of quaternion spinors
Abstract
It is shown that dyad vectors on a local domain of complex-number valued surface, when squared, form a set of four quaternion algebra units. A model of proto-particle is built by the dyad's rotation and stretching; this transformation violates metric properties of the surface, but the defect is cured by a stability condition for normalization functional over an abstract space. If the space is the physical one then the stability condition is precisely Schrodinger equation; separated real and imaginary parts of the condition are respectively equation of mass conservation and Hamilton-Jacoby equation. A 3D particle (composed of the proto-particle's parts) has to be conceived as a rotating massive point, its Lagrangian automatically becoming that of relativistic classical particle, energy and momentum proportional to Planck constant. In uence of a vector field onto the particle's propagation causes automatic appearance of Pauli spin term in Schrodinger equation.
Keywords
Cite
@article{arxiv.1212.6005,
title = {Pre-geometric structure of quantum and classical particles in terms of quaternion spinors},
author = {Alexander P. Yefremov},
journal= {arXiv preprint arXiv:1212.6005},
year = {2016}
}
Comments
10 pages