تقرير
An algebraic formulation of nonassociative quantum mechanics
| العنوان: | An algebraic formulation of nonassociative quantum mechanics |
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| المؤلفون: | Schupp, Peter, Szabo, Richard J. |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics High Energy Physics - Theory Mathematical Physics Quantum Physics |
| مصطلحات موضوعية: | Quantum Physics, High Energy Physics - Theory, Mathematical Physics, Mathematics - Rings and Algebras |
| الوصف: | 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 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.03647 |
| رقم الأكسشن: | edsarx.2311.03647 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |