dorsal/arxiv
View SchemaHypercomplex quantum mechanics
| Authors | L. P. Horwitz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9602001 |
| URL | https://arxiv.org/abs/quant-ph/9602001 |
| DOI | 10.1007/BF02058638 |
Abstract
The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective geometry of the weakly modular orthocomplemented lattice of propositions may be imbedded in a complex Hilbert space; this is the structure which has traditionally been used. This paper reviews some work which has been devoted to generalizing the target space of this imbedding to Hilbert modules of a more general type. In particular, detailed discussion is given of the simplest generalization of the complex Hilbert space, that of the quaternion Hilbert module.
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"abstract": "The fundamental axioms of the quantum theory do not explicitly identify the\nalgebraic structure of the linear space for which orthogonal subspaces\ncorrespond to the propositions (equivalence classes of physical questions). The\nprojective geometry of the weakly modular orthocomplemented lattice of\npropositions may be imbedded in a complex Hilbert space; this is the structure\nwhich has traditionally been used. This paper reviews some work which has been\ndevoted to generalizing the target space of this imbedding to Hilbert modules\nof a more general type. In particular, detailed discussion is given of the\nsimplest generalization of the complex Hilbert space, that of the quaternion\nHilbert module.",
"arxiv_id": "quant-ph/9602001",
"authors": [
"L. P. Horwitz"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/BF02058638",
"title": "Hypercomplex quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/9602001"
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