Geometric and algebraic approaches to quantum theory

被引:7
作者
Schwarz, A. [1 ]
机构
[1] Univ Calif Davis, Dept Math, Davis, CA 95616 USA
关键词
FORMALISM;
D O I
10.1016/j.nuclphysb.2021.115601
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
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. (C) 2021 The Author(s). Published by Elsevier B.V.
引用
收藏
页数:22
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