From Mass-Shell Factorisation to Spin: An Attempt at a Matrix-Valued Liouville Framework for Relativistic Classical and Quantum Phase-Spacetime
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917503621398528 |
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| author | Everitt, Mark J. |
| author_facet | Everitt, Mark J. |
| contents | Here we argue that spinor structure arises naturally if relativistic statistical mechanics is formulated directly on phase spacetime. Requiring a first-order phase-spacetime description that retains both mass-shell branches leads to a Clifford factorisation of the relativistic constraint and hence to a $4\times4$ spinor-matrix distribution function. We show that deformation quantisation leads to a phase-space formulation of spin quantum mechanics. We argue that projection onto positive- and negative-energy sectors recovers the standard relativistic classical transport equations in the appropriate scalar limits, while the corresponding left- and right- stargenvalue equations reproduce the constraint structure of the Dirac-Wigner formulation. The result is a phase-space route from relativistic statistical mechanics to spinor quantum mechanics, in which spin algebra emerges as the internal structure required by any relativistic statistical theory containing both mass-shell branches and the dimensions of angular momentum from quantum non-locality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Mass-Shell Factorisation to Spin: An Attempt at a Matrix-Valued Liouville Framework for Relativistic Classical and Quantum Phase-Spacetime Everitt, Mark J. Quantum Physics Classical Physics Here we argue that spinor structure arises naturally if relativistic statistical mechanics is formulated directly on phase spacetime. Requiring a first-order phase-spacetime description that retains both mass-shell branches leads to a Clifford factorisation of the relativistic constraint and hence to a $4\times4$ spinor-matrix distribution function. We show that deformation quantisation leads to a phase-space formulation of spin quantum mechanics. We argue that projection onto positive- and negative-energy sectors recovers the standard relativistic classical transport equations in the appropriate scalar limits, while the corresponding left- and right- stargenvalue equations reproduce the constraint structure of the Dirac-Wigner formulation. The result is a phase-space route from relativistic statistical mechanics to spinor quantum mechanics, in which spin algebra emerges as the internal structure required by any relativistic statistical theory containing both mass-shell branches and the dimensions of angular momentum from quantum non-locality. |
| title | From Mass-Shell Factorisation to Spin: An Attempt at a Matrix-Valued Liouville Framework for Relativistic Classical and Quantum Phase-Spacetime |
| topic | Quantum Physics Classical Physics |
| url | https://arxiv.org/abs/2505.03551 |