Keywords
- Quantum Mechanic
- Free Field
- Lower Eigenvalue
- Canonical Commutation Relation
- Tensor Product Space
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References
von Neumann, J.; Math. Ann. 104 570 (1931).
Garding, L. and Wightman, A.S.; Proc. Nat. Acad. Sci. 40 622 (1954)
Currently progress has been made in this direction. For two dimensional space-time and even degree polynomial interactions this program was carried out by J. Glimm, A. Jaffe and others.
F(α) is separable only in the non-standard sense.
This program was carried out for the model in ref. 3 in Kelemen, P.J. and Robinson, A.; J.M.P. 13 (Dec. 1972).
Earlier, the exponentiated form of this commutation relation was given, because q and p are unbounded operators and we wished to avoid the question of their domains.
von Neumann.; Compos. Math. 6 1 (1939).
We are assuming that the interaction term used in the Hamiltonian allows the realization of the canonical commutation relations on an infinite tensor product space. A large class of representations of the canonical commutation relations cannot be realized on an infinite tensor product space.
Streater, R.F. and Wightman, A.S.; PCT, Spin & Statistics and All That, W.A. Benjamin, Inc., New York (1964).
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© 1974 Springer-Verlag
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Kelemen, P.J. (1974). Quantum mechanics, quantum field theory and hyper-quantum mechanics. In: Hurd, A., Loeb, P. (eds) Victoria Symposium on Nonstandard Analysis. Lecture Notes in Mathematics, vol 369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066006
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DOI: https://doi.org/10.1007/BFb0066006
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