Abstract
A recent work on the many-body problem in modern physics begins with the following paragraph:
A reasonable starting point for a discussion of the many-body problem might be the question of how many bodies are required before we have a problem. Prof. G. E. Brown has pointed out that, for those interested in exact solutions, this can be answered by a look at history. In eighteenth-century Newtonian mechanics, the three-body problem was insoluble. With the birth of general relativity around 1910 and quantum electrodynamics in 1930, the two- and one-body problems became insoluble. And within modern quantum field theory, the problem of zero bodies (the vacuum) is insoluble. So, if we are out after exact solutions, no bodies at all is already too many.1
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Notes
R. D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem, McGraw-Hill, New York, 1967.
J. S. Bell, D. Bohm and J. Bub, Reviews of Modem Physics 38 (1966) (series of three papers).
J. M. Jauch and C. Piron, Helvetica Physica Acta 37 (1964) 293.
Cf. Letters to the Editor, Reviews of Modern Physics 40 (1968) 228ff.
A. R. Marlow, Journal of Mathematical Physics (submitted for publication).
A. R. Marlow, Journal of Mathematical Physics (submitted for publication).
G. Birkhoff and J. von Neumann, Annals of Mathematics 37 (1936), 823.
G. W. Mackey, The Mathematical Foundations of Quantum Mechanics, Benjamin, New York, 1963.
Piron, Helvetica Physica Acta 37 (1964), 439.
See note 8, p. 66.
For the further development of the quantum mechanical model, cf. note 8, pp. 71 ff.
For a full discussion of this point, see S. P. Gudder, Journal of Mathematical Physics 8 (1967), 1848 and our note 5, footnote 1.
Due to a suggestion of Dr. Abner Shimony, the general proof of the existence of embedding is independent of the countability assumption (A).
At least some of this multiplicity is removed in the C*-algebra approach to quantum theory; for an account of this approach, see D. Kastler, pp. 179–191 in the volume edited by W. Martin and I. Segal, Analysis in Function Space, MIT Press, Cambridge, Mass., 1964.
This modifies and sharpens somewhat an interesting comparison offered by D. Bohm and J. Bub, Reviews of Modern Physics 40 (1968), 235.
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© 1974 D. Reidel Publishing Company, Dordrecht, Holland
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Marlow, A.R. (1974). Implications of a New Axiom Set for Quantum Logic. In: Cohen, R.S., Wartofsky, M.W. (eds) Logical and Epistemological Studies in Contemporary Physics. Boston Studies in the Philosophy of Science, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2656-7_12
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DOI: https://doi.org/10.1007/978-94-010-2656-7_12
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