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)


Quantum Mechanic Free Field Lower Eigenvalue Canonical Commutation Relation Tensor Product Space 
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  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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