Hilbert's 6th Problem and Axiomatic Quantum Field Theory

Perspectives on Science 22 (1):80-97 (2014)
Authors
Miklós Rédei
London School of Economics
Abstract
This paper has two parts, a historical and a systematic. In the historical part it is argued that the two major axiomatic approaches to relativistic quantum field theory, the Wightman and Haag-Kastler axiomatizations, are realizations of the program of axiomatization of physical theories announced by Hilbert in his 6th of the 23 problems discussed in his famous 1900 Paris lecture on open problems in mathematics, if axiomatizing physical theories is interpreted in a soft and opportunistic sense suggested in 1927 by Hilbert, Nordheim, and von Neumann. To show this, Section 2 recalls first some of Hilbert's views about the axiomatic approach to physical theories as these were formulated in his 6th problem. It will be ..
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DOI 10.1162/posc_a_00119
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Why John von Neumann Did Not Like the Hilbert Space Formalism of Quantum Mechanics (and What He Liked Instead).Miklos Rédei - 1996 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 27 (4):493-510.
The Subtleties of Entanglement and its Role in Quantum Information Theory.Rob Clifton - 2001 - Proceedings of the Philosophy of Science Association 2002 (3):S150-S167.

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