Abstract
It is shown that there exists a selfadjoint Hamilton operator corresponding to the interactionH (a)0 +H (b)0 +∫Φ + b (x)Φ a (x)Φ − b (x)d 3 x, wherea andb denote two types of scalar particles. We discuss the scattering theory of this operator.
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References
Cannon, J. T.: Field theoretic properties of Nelson's model. Princeton University, Thesis 1968.
Eckmann, J.-P.: A theorem on kernels of superrenormalizable theories. Preprint.
-- Hamiltonians of persistent interactions. Université de Genève, Thesis 1970.
Friedrichs, K. O.: Perturbation of spectra in Hilbert space. Providence: AMS, 1965.
Glimm, J.: Yukawa coupling of quantum fields in two dimensions I. Commun. Math. Phys.5, 343 (1967).
Hepp, K.: Théorie de la renormalisation; Lecture Notes in Physics Vol. 2. Berlin, Heidelberg, New York: Springer 1969.
Jaffe, A.: Constructive quantum field theory. Lecture Notes ETH Zürich (1968).
Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966.
Nelson, E.: Interaction of nonrelativistic particles with a quantized scalar field. J. Math. Phys.5, 1190 (1964).
Polya, G.: Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen. Acta Math.68, 145 (1937).
Schrader, R.: On the existence of a local Hamiltonian in the Galilean invariant Lee model. Commun. Math. Phys.10, 155 (1968).
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Work partially supported by the Swiss National Science Foundation.
This paper contains results from the author's Ph. D. Thesis [3].
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Eckmann, J.P. A model with persistent vacuum. Commun.Math. Phys. 18, 247–264 (1970). https://doi.org/10.1007/BF01649435
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DOI: https://doi.org/10.1007/BF01649435