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Quantum theory and functional analysis

Landsman, Klaas (2019) Quantum theory and functional analysis. [Preprint]

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Abstract

Quantum theory and functional analysis were created and put into essentially their final form during similar periods ending around 1930. Each was also a key outcome of the major revolutions that both physics and mathematics as a whole underwent at the time. This paper studies their interaction in this light, emphasizing the leading roles played by Hilbert in preparing the ground and by von Neumann in bringing them together during the crucial year of 1927, when he gave the modern, abstract definition of a Hilbert space and applied this concept to quantum mechanics (consolidated in his famous monograph from 1932).
Subsequently, I give a very brief overview of three areas of
functional analysis that have had fruitful interactions with quantum theory since 1932, namely unbounded operators, operator algebras, and distributions. The paper closes with some musings about the role of functional analysis in actual physics.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Landsman, Klaaslandsman@math.ru.nl
Keywords: Quantum theory, functional analysis, history, mathematical physics
Subjects: Specific Sciences > Mathematics > History
Specific Sciences > Physics > Quantum Mechanics
Depositing User: Nicolaas P. Landsman
Date Deposited: 04 Nov 2019 19:56
Last Modified: 04 Nov 2019 19:56
Item ID: 16613
Subjects: Specific Sciences > Mathematics > History
Specific Sciences > Physics > Quantum Mechanics
Date: 3 November 2019
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/16613

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