Abstract
We extend to arbitrary dimension the proof by Guenin that the time-evolution is an automorphism group of the local algebras, if the interaction Hamiltonian is a space-integral of a bounded local density with finite range.
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Segal, I. E.: Quasi-finiteness of the interaction Hamiltonian of certain quantum fields. Ann. Math.72, 594 (1960).
Haag, R.: Colloques sur les problèmes mathématiques de la théorie quantique des champs. Paris: Centre Nationale des Recherches Scientifiques 1959;
Haag, R., Schroer, B.: Postulates of quantum field theory. J. Math. Phys.3, 248 (1962);
Haag, R., Kastler, D.: An algebraic approach to quantum field theory. J. Math. Phys.5, 848 (1964).
Guenin, M.: On the interaction picture. Commun. Math. Phys.3, 120 (1966).
Streater, R. F.: The Heisenberg ferromagnet as a quantum field theory. Commun. Math. Phys.6, 233 (1967).
—— On certain non-relativistic quantized fields. Commun. Math. Phys.7, 93 (1968).
See Yosida, K.: Functional analysis, p. 132. Berlin-Heidelberg-New York: Springer 1965.
Haag, R.: On quantum field theory. Dan. Mat. Fys. Medd.29, 12 (1955).
Robinson, D. W.: Commun. Math. Phys.7, 337 (1968).
Ruelle, D.: Statistical mechanics. New York: Benjamin 1969.
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Streater, R.F., Wilde, I.F. The time evolution of quantized fields with bounded quasi-local interaction density. Commun.Math. Phys. 17, 21–32 (1970). https://doi.org/10.1007/BF01649581
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DOI: https://doi.org/10.1007/BF01649581