Measurements and mathematical formalism of quantum mechanics

被引:0
作者
Slavnov, D. A. [1 ]
机构
[1] Moscow MV Lomonosov State Univ, Moscow 119992, Russia
关键词
D O I
10.1134/S1063779607020013
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
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.
引用
收藏
页码:147 / 176
页数:30
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