An algebraic formulation of nonassociative quantum mechanics

Autor:	Schupp, Peter, Szabo, Richard J.
Rok vydání:	2023
Předmět:	Quantum Physics High Energy Physics - Theory Mathematical Physics Mathematics - Rings and Algebras
Druh dokumentu:	Working Paper
Popis:	We develop a version of quantum mechanics that can handle nonassociative algebras of observables and which reduces to standard quantum theory in the traditional associative setting. Our algebraic approach is naturally probabilistic and is based on using the universal enveloping algebra of a general nonassociative algebra to introduce a generalized notion of associative composition product. We formulate properties of states together with notions of trace, and use them to develop GNS constructions. We describe Heisenberg and Schr\"odinger pictures of completely positive dynamics, and we illustrate our formalism on the explicit examples of finite-dimensional matrix Jordan algebras as well as the octonion algebra. Comment: 35 pages; v2: minor corrections; v3: minor changes, Conclusions section added; Final version to appear in Journal of Physics A
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.03647 Zobrazit plný text záznamu View this record from Arxiv