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Quantum mechanics, quantum field theory and hyper-quantum mechanics

  • Peter J. Kelemen
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 369)

Keywords

Quantum Mechanic Free Field Lower Eigenvalue Canonical Commutation Relation Tensor Product Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    von Neumann, J.; Math. Ann. 104 570 (1931).MathSciNetCrossRefGoogle Scholar
  2. 2.
    Garding, L. and Wightman, A.S.; Proc. Nat. Acad. Sci. 40 622 (1954)MathSciNetCrossRefGoogle Scholar
  3. 3.
    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.Google Scholar
  4. 4.
    F(α) is separable only in the non-standard sense.Google Scholar
  5. 5.
    This program was carried out for the model in ref. 3 in Kelemen, P.J. and Robinson, A.; J.M.P. 13 (Dec. 1972).Google Scholar
  6. 6.
    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.Google Scholar
  7. 7.
    von Neumann.; Compos. Math. 6 1 (1939).Google Scholar
  8. 8.
    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.Google Scholar
  9. 9.
    Streater, R.F. and Wightman, A.S.; PCT, Spin & Statistics and All That, W.A. Benjamin, Inc., New York (1964).zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Peter J. Kelemen
    • 1
  1. 1.New York University, University HeightsBronx

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