Abstract
TheP(ϕ)2 interaction with the periodic boundary conditions is considered. It is shown that the energy-momentum spectrum lies in the forward light cone. As a consequence, this result implies that theP(ϕ)2 theory in the infinite volume with the periodic boundary conditions is Lorentz invariant.
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Glimm, J., Jaffe, A.: Energy-momentum spectrum and vacuum expectation values in quantum field theory. J. Math. Phys.11, 3335–3338 (1970); Erratum: Math. Rev.43, 1697 (1972)
Seiler, E., Simon, B.: Nelson's symmetry and all that in the Yukawa2 and ø 43 field theories. Ann. Phys.97, 470–518 (1976)
Glimm, J., Jaffe, A.: The energy-momentum spectrum and vacuum expectation values in quantum field theory, II. Commun. math. Phys.22, 1–22 (1971)
Streater, R.F.: Connection between the spectrum condition and the Lorentz invariance ofP(ϕ)2. Commun. math. Phys.26, 109–120 (1972)
Bogoliubov, N.N., Vladimirov, V.S.: Representations ofn-point functions (In Russian). In: Trudi Matematicheskogo Instituta imeni Steklova, Vol. 112, pp. 5–21. Moscow: Nauka 1971
Heifets, E.P.: The existence of the:expϕ:4 quantum field theory in a finite volume. Phys. Lett.59B, 61–62 (1975)
Heifets, E.P., Osipov, E.P.: The energy-momentum spectrum in the Yukawa2 quantum field theory. Commun. math. Phys., to be published
Kurosch, A.G.: General Algebra. New York: Chelsea 1963
Streater, R.F., Wightman, A.S.:PCT, spin and statistics and all that. New York—Amsterdam: Benjamin 1964
Dixmier, J.: Les algèbres d'opérateurs dans l'espace hilbertien (Algèbres de von Neumann). Paris: Cauthier—Villars 1957
Simon, B., Hoegh-Krohn, R.: Hypercontractive semigroups and two dimensional self-coupled Bose fields. J. Funct. Anal.9, 121–180 (1972)
Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966
Naimark, M. A.: Linear differential operators. Moscow: Nauka 1969
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Communicated by A. Jaffe
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Heifets, E.P., Osipov, E.P. The energy-momentum spectrum in theP(ϕ)2 quantum field theory. Commun.Math. Phys. 56, 161–172 (1977). https://doi.org/10.1007/BF01611501
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DOI: https://doi.org/10.1007/BF01611501