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Generalizing Stratonovich–Weyl Axioms for Composite Systems

A. Khvedelidze

Abstract The statistical model of quantum mechanics is based on the mapping between operators on the Hilbert space and functions on the phase space. This map can be implemented by an operator that satisfies physically motivated Stratonovich–Weyl axioms. Arguments are given in favour of a certain extension of the axioms, provided that there is a priori knowledge about the composite nature of the quantum system.

arXiv:2209.13298Physics of Particles and NucleiNov 29, 20231 citation

Importance of Hilbert Space In Quantum Mechanics

Ashoke Das, Sahın Injamamul ISLAM

International Journal of Mathematics Trends and TechnologyJan 25, 20201 citation

Об обобщении аксиом Стратоновича–Вейля для составных систем: Аннотации

A. Khvedelidze

The statistical model of quantum mechanics is based on the mapping between operators on the Hilbert space and functions on the phase space. This map can be implemented by an operator that satisfies physically motivated Stratonovich–Weyl axioms. Arguments are given in favour of a certain extension of the axioms, provided that there is a priori knowledge about the composite nature of the quantum system.

ФИЗИКА ЭЛЕМЕНТАРНЫХ ЧАСТИЦ И АТОМНОГО ЯДРАMay 31, 20240 citations

Why and whence the Hilbert space in quantum theory?

Yu. V. Brezhnev

arXiv:2110.05932Journal of Geometry and PhysicsFeb 17, 20235 citations

Introduction to Quantum Mechanics

Eduardo J. S. Villaseñor, Rui Loja Fernandes, Roger Picken

The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.

arXiv:0804.3728AIP conference proceedingsJan 1, 200852 citations

Quantum Physics in Non-Separable Hilbert Spaces

John Earman

In Mathematical Foundations of Quantum Mechanics (1932) von Neumann made separability of Hilbert space an axiom. Subsequent work in mathematics (some of it by von Neumann himself) investigated non-separable Hilbert spaces, and mathematical physicists have sometimes made use of them. This note discusses some of the problems that arise in trying to treat quantum systems with non-separable spaces. Some of the problems are "merely technical" but others point to interesting foundations issues for quantum theory, both in its abstract mathematical form and its applications to physical systems. Nothing new or original is attempted here. Rather this note aims to bring into focus some issues that have for too long remained on the edge of consciousness for philosophers of physics.In Mathematical Foundations of Quantum Mechanics (1932) von Neumann made separability of Hilbert space an axiom. Subsequent work in mathematics (some of it by von Neumann himself) investigated non-separable Hilbert spaces, and mathematical physicists have sometimes made use of them. This note discusses some of the problems that arise in trying to treat quantum systems with non-separable spaces. Some of the problems are "merely technical" but others point to interesting foundations issues for quantum theory, both in its abstract mathematical form and its applications to physical systems. Nothing new or original is attempted here. Rather this note aims to bring into focus some issues that have for too long remained on the edge of consciousness for philosophers of physics.

Nov 6, 202016 citations

Possible a priori motivations for the use of Hilbert spaces in Quantum Mechanics

Abstract

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Possible a priori motivations for the use of Hilbert spaces in Quantum Mechanics

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