dorsal/arxiv
View SchemaAlgebraic Quantum Mechanics and Pregeometry
| Authors | D. J. Bohm, P. G. Davies, B. J. Hiley |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612002 |
| URL | https://arxiv.org/abs/quant-ph/0612002 |
| DOI | 10.1063/1.2158735 |
Abstract
We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford Algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra in a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra.
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"abstract": "We discuss the relation between the q-number approach to quantum mechanics\nsuggested by Dirac and the notion of \"pregeometry\" introduced by Wheeler. By\nassociating the q-numbers with the elements of an algebra and regarding the\nprimitive idempotents as \"generalized points\" we suggest an approach that may\nmake it possible to dispense with an a priori given space manifold. In this\napproach the algebra itself would carry the symmetries of translation,\nrotation, etc. Our suggestion is illustrated in a preliminary way by using a\nparticular generalized Clifford Algebra proposed originally by Weyl, which\napproaches the ordinary Heisenberg algebra in a suitable limit. We thus obtain\na certain insight into how quantum mechanics may be regarded as a purely\nalgebraic theory, provided that we further introduce a new set of\n\"neighbourhood operators\", which remove an important kind of arbitrariness that\nhas thus far been present in the attempt to treat quantum mechanics solely in\nterms of a Heisenberg algebra.",
"arxiv_id": "quant-ph/0612002",
"authors": [
"D. J. Bohm",
"P. G. Davies",
"B. J. Hiley"
],
"categories": [
"quant-ph",
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"math.QA"
],
"doi": "10.1063/1.2158735",
"title": "Algebraic Quantum Mechanics and Pregeometry",
"url": "https://arxiv.org/abs/quant-ph/0612002"
},
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