dorsal/arxiv
View SchemaCommon Space of Spin and Spacetime
| Authors | Wei Min Jin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409011 |
| URL | https://arxiv.org/abs/quant-ph/0409011 |
| DOI | 10.1007/s10702-005-6115-z |
| Journal | Found.Phys.Lett. 18 (2005) 243-258 |
Abstract
Given Lorentz invariance in Minkowski spacetime, we investigate a common space of spin and spacetime. To obtain a finite spinor representation of the non-compact homogeneous Lorentz group including Lorentz boosts, we introduce an indefinite inner product space (IIPS) with a normalized positive probability. In this IIPS, the common momentum and common variable of a massive fermion turn out to be ``doubly strict plus-operators''. Due to this nice property, it is straightforward to show an uncertainty relation between fermion mass and proper time. Also in IIPS, the newly-defined Lagrangian operators are self-adjoint, and the fermion field equations are derivable from the Lagrangians. Finally, the nonlinear QED equations and Lagrangians are presented as an example.
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"abstract": "Given Lorentz invariance in Minkowski spacetime, we investigate a common\nspace of spin and spacetime. To obtain a finite spinor representation of the\nnon-compact homogeneous Lorentz group including Lorentz boosts, we introduce an\nindefinite inner product space (IIPS) with a normalized positive probability.\nIn this IIPS, the common momentum and common variable of a massive fermion turn\nout to be ``doubly strict plus-operators\u0027\u0027. Due to this nice property, it is\nstraightforward to show an uncertainty relation between fermion mass and proper\ntime. Also in IIPS, the newly-defined Lagrangian operators are self-adjoint,\nand the fermion field equations are derivable from the Lagrangians. Finally,\nthe nonlinear QED equations and Lagrangians are presented as an example.",
"arxiv_id": "quant-ph/0409011",
"authors": [
"Wei Min Jin"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th"
],
"doi": "10.1007/s10702-005-6115-z",
"journal_ref": "Found.Phys.Lett. 18 (2005) 243-258",
"title": "Common Space of Spin and Spacetime",
"url": "https://arxiv.org/abs/quant-ph/0409011"
},
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