dorsal/arxiv
View SchemaAlgebraic-statistical approach to quantum mechanics
| Authors | D. A. Slavnov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0101139 |
| URL | https://arxiv.org/abs/quant-ph/0101139 |
Abstract
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative algebra (observables) and the nonlinear functionals on this algebra (physical states) are used as the primary constituents. The functionals associate with results of a particular measurement. It is suggested to consider certain ensembles of the physical states as quantum states of the standart quantum mechanics. It is shown that in such scheme the mathematical formalism of the standart quantum mechanics can be reproduced completely.
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"abstract": "It is proposed the scheme of quantum mechanics, in which a Hilbert space and\nthe linear operators are not primary elements of the theory. Instead of it\ncertain variant of the algebraic approach is considered. The elements of\nnoncommutative algebra (observables) and the nonlinear functionals on this\nalgebra (physical states) are used as the primary constituents. The functionals\nassociate with results of a particular measurement. It is suggested to consider\ncertain ensembles of the physical states as quantum states of the standart\nquantum mechanics. It is shown that in such scheme the mathematical formalism\nof the standart quantum mechanics can be reproduced completely.",
"arxiv_id": "quant-ph/0101139",
"authors": [
"D. A. Slavnov"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"title": "Algebraic-statistical approach to quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0101139"
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