Geometric and algebraic approaches to quantum theory

We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of complex systems. The equations of motion and the formulas for prob...

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Autor principal:	A. Schwarz
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/1c004ce0edb249c2b4d3bc738140aca0
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spelling	oai:doaj.org-article:1c004ce0edb249c2b4d3bc738140aca02021-12-04T04:32:57ZGeometric and algebraic approaches to quantum theory0550-321310.1016/j.nuclphysb.2021.115601https://doaj.org/article/1c004ce0edb249c2b4d3bc738140aca02021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S0550321321002984https://doaj.org/toc/0550-3213We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of complex systems. The equations of motion and the formulas for probabilities of physical quantities are analyzed. A heuristic proof of decoherence in our setting is used to justify the formulas for probabilities. We show that any physical theory can be obtained from classical theory if we restrict the set of observables. This remark can be used to construct models with any prescribed group of symmetries; one can hope that this construction leads to new interesting models that cannot be build in the conventional framework.The geometric approach can be used to formulate quantum theory in terms of Jordan algebras, generalizing the algebraic approach to quantum theory. The scattering theory can be formulated in geometric approach.A. SchwarzElsevierarticleNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENNuclear Physics B, Vol 973, Iss , Pp 115601- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 A. Schwarz Geometric and algebraic approaches to quantum theory
description	We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of complex systems. The equations of motion and the formulas for probabilities of physical quantities are analyzed. A heuristic proof of decoherence in our setting is used to justify the formulas for probabilities. We show that any physical theory can be obtained from classical theory if we restrict the set of observables. This remark can be used to construct models with any prescribed group of symmetries; one can hope that this construction leads to new interesting models that cannot be build in the conventional framework.The geometric approach can be used to formulate quantum theory in terms of Jordan algebras, generalizing the algebraic approach to quantum theory. The scattering theory can be formulated in geometric approach.
format	article
author	A. Schwarz
author_facet	A. Schwarz
author_sort	A. Schwarz
title	Geometric and algebraic approaches to quantum theory
title_short	Geometric and algebraic approaches to quantum theory
title_full	Geometric and algebraic approaches to quantum theory
title_fullStr	Geometric and algebraic approaches to quantum theory
title_full_unstemmed	Geometric and algebraic approaches to quantum theory
title_sort	geometric and algebraic approaches to quantum theory
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/1c004ce0edb249c2b4d3bc738140aca0
work_keys_str_mv	AT aschwarz geometricandalgebraicapproachestoquantumtheory
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Geometric and algebraic approaches to quantum theory

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