Spin Axioms in Relativistic Continuum Physics

TL;DR

This paper discusses the structure of relativistic spin tensors, introduces axioms that relate basic and constitutive spin fields, and examines implications for different fluid models in continuum physics.

Contribution

It proposes two spin axioms that relate basic and constitutive spin fields, clarifying their material independence and impact on fluid models.

Findings

Empirical basic spin fields are 3, constitutive fields are 9.

Two spin axioms relate these fields without mixing basic and constitutive properties.

Violating axioms may introduce unphysical material properties.

Abstract

The 24 components of the relativistic spin tensor consist of 3+3 basic spin fields and 9+9 constitutive fields. Empirically only 3 basic spin fields and 9 constitutive fields are known. This empirem can be expressed by two spin axioms, one of them identifying 3 spin fields, and the other one 9 constitutive fields to each other. This identification by the spin axioms is material-independent and does not mix basic spin fields with constitutive properties. The approaches to the Weyssenhoff fluid and the Dirac-electron fluid found in literature are discussed with regard to these spin axioms. The conjecture is formulated, that another reduction from 6 to 3 basic spin fields which does not obey the spin axioms introduces special material properties by not allowed mixing of constitutive and basic fields.