Isospin from Spin by Compositenes

TL;DR

This paper introduces a geometrical approach to generate internal isospin from non-local bound states, linking Lorentz group rotations to isospin via Clifford algebra and gauge theory, extending beyond traditional group theory.

Contribution

It presents a novel geometrical model that derives isospin from spin through non-local bound states and gauge theory, using Clifford algebraic methods.

Findings

Bound states characterized by spinor triples or pairs, forming isospinors.

Derivation of an isospin gauge theory from covariant gauge coupling.

Method applicable beyond isospin to other internal symmetries.

Abstract

We propose a new method to generate the internal isospin degree of freedom by non-local bound states. This can be seen as motivated by Bargmann-Wigner like considerations, which originated from local spin coupling. However, our approach is not of purely group theoretical origin, but emerges from a geometrical model. The rotational part of the Lorentz group can be seen to mutate into the internal iso-group under some additional assumptions. The bound states can thereafter be characterized by either a triple of spinors (\xi_1, \xi_2, \eta) or a pair of an average spinor and a ``gauge'' transformation (\phi, R). Therefore, this triple can be considered to be an isospinor. Inducing the whole dynamics from the covariant gauge coupling we arrive at an isospin gauge theory and its Lagrangian formulation. Clifford algebraic methods, especially the Hestenes approach to the geometric meaning of spinors, are the most useful concepts for such a development. The method is not restricted to isospin, which served as an example only.