dorsal/arxiv
View SchemaQuantization as a dimensional reduction phenomenon
| Authors | E. Gozzi, D. Mauro |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0601209 |
| URL | https://arxiv.org/abs/quant-ph/0601209 |
| DOI | 10.1063/1.2219360 |
| Journal | AIP Conf.Proc. 844 (2006) 158-176 |
Abstract
Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three dimensional supermanifold. Quantization is then achieved by a process of dimensional reduction of this supermanifold. We prove that this procedure is equivalent to the well-known method of geometric quantization.
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"abstract": "Classical mechanics, in the operatorial formulation of Koopman and von\nNeumann, can be written also in a functional form. In this form two Grassmann\npartners of time make their natural appearance extending in this manner time to\na three dimensional supermanifold. Quantization is then achieved by a process\nof dimensional reduction of this supermanifold. We prove that this procedure is\nequivalent to the well-known method of geometric quantization.",
"arxiv_id": "quant-ph/0601209",
"authors": [
"E. Gozzi",
"D. Mauro"
],
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"quant-ph",
"hep-th"
],
"doi": "10.1063/1.2219360",
"journal_ref": "AIP Conf.Proc. 844 (2006) 158-176",
"title": "Quantization as a dimensional reduction phenomenon",
"url": "https://arxiv.org/abs/quant-ph/0601209"
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