Abstract
Particles are shown to exist for a.e. value of the mass in single phase φ4 lattice and continuum field theories and nearest neighbor Ising models. The particles occur in the form of poles at imaginary (Minkowski) momenta of the Fourier transformed two point function. The new inequalitydm 2/dσ≦Z, where σ=m 20 is a bare mass2 andZ is the strength of the particle pole, is basic to our method. This inequality implies inequalities for critical exponents.
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References
Baker, G.: Self interacting boson quantum field theory and the thermodynamic limit ind dimensions. J. Math. Phys.16, 1324–1346 (1975)
Coleman, S.: Secret Symmetry: An introduction to spontaneous symmetry breakdown and guage fields. 1973 Erice Summer School of Physics
Fisher, M.: Rigorous Inequalities for critical-point correlation exponents. Phys. Rev.180, 594–600 (1969)
Fröhlich, J., Simon, B., Spencer, T.: A new method for the analysis of phase transitions and spontaneous breaking of discrete and continuous symmetries. Phys. Rev. Lett.36, 804–806 (1976)
Fröhlich, J., Simon, B.: Pure states for generalP(φ)2 theories: Construction, regularity and variational equality. Ann. Math., to appear
Glimm, J., Jaffe, A.: A remark on the existence of φ 44 . Phys. Rev. Lett.33, 440–442 (1974)
Glimm, J., Jaffe, A.: The φ 42 quantum field theory in the single phase region: Differentiability of the mass and bounds on critical exponents. Phys. Rev. D10, 536–539 (1974)
Glimm, J., Jaffe, A.: Three particle structure of φ4 interactions and the scaling limit. Phys. Rev. D11, 2816–2827 (1975)
Glimm, J., Jaffe, A.: Critical problems in quantum fields, International Colloquium on Mathematical Methods of Quantum Field Theory, Marseille, June 1975
Glimm, J., Jaffe, A.: Critical exponents and renormalization in the φ4 scaling limit, Conference on quantum dynamics: Models and mathematics. Acta Phys. Austriaca Suppl. XVI (1975)
Glimm, J., Jaffe, A.: Particles and scaling for lattice fields and Ising models. Commun. math. Phys.51, 1–14 (1976)
Rosen, J.: Mass renormalization for lattice λφ 42 fields. Adv. Math. (to appear)
Rosen, J.: The Ising limit of φ4 lattice fields. The Rockefeller University (preprint)
Schrader, R.: A possible constructive approach to φ 44 I, III. Commun. math. Phys.49, 131–154 (1976);50, 97–102 (1976)
Kato, J.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966
Glimm, J., Jaffe, A.: A λφ4 Quantum field theory without cutoffs. I. Phys. Rev.176, 1945–1951 (1968) and Singular perturbations of self adjoint operators. Comm. Pure Appl. Math.22, 401–414 (1969)
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Communicated by R. Haag
Supported in part by the National Science Foundation under grant PHY 76-17191
Supported in part by the National Science Foundation under grant MPS 75-21212
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Glimm, J., Jaffe, A. Critical exponents and elementary particles. Commun.Math. Phys. 52, 203–209 (1977). https://doi.org/10.1007/BF01609482
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DOI: https://doi.org/10.1007/BF01609482