Advertisement

Communications in Mathematical Physics

, Volume 57, Issue 1, pp 31–50 | Cite as

The energy-momentum spectrum in the Yukawa2 quantum field theory

  • Edward P. Heifets
  • Edward P. Osipov
Article

Abstract

We prove that the Yukawa2 quantum field theory with periodic boundary conditions satisfies the spectral condition, i.e., the joint spectrum of the energy operatorH and the momentum operatorP is contained in the forward cone. In addition, the ϕ-bound is obtained.

Keywords

Boundary Condition Neural Network Statistical Physic Field Theory Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Seiler, E., Simon, B.: Nelson's symmetry and all that in the Yukawa2 and φ34 Field Theories. Ann. Phys.97, 470–518 (1976)Google Scholar
  2. 2.
    Glimm, J.: The Yukawa coupling of quantum field in two dimensions, II. Commun. math. Phys.8, 12–25 (1967)Google Scholar
  3. 3.
    Glimm, J., Jaffe, A.: Quantum field theory models. In: Statistical mechanics and quantum field theory, pp. 1–108. Les Houches 1970, (ed. C. DeWitt, R. Stora). New York: Gordon and Breach 1971Google Scholar
  4. 4.
    Kurosch, A. G.: General algebra. New York: Chelsea 1963Google Scholar
  5. 5.
    Bogolubov, N. N., Shirkov, D. V.: Introduction to the theory of quantized fields. New York: Interscience Publishers 1959Google Scholar
  6. 6.
    Seiler, E., Simon, B.: Bounds in the Yukawa2 quantum field theory: Upper bound on the pressure, Hamiltonian bound and linear lower bound. Commun. math. Phys.45, 99–114 (1975)Google Scholar
  7. 7.
    Glimm, J., Jaffe, A.: Self-adjointness of the Yukawa2 Hamiltonian. Ann. Phys.60, 321–383 (1970)Google Scholar
  8. 8.
    Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966Google Scholar
  9. 9.
    Simon, B., Hoegh-Krohn, R.: Hypercontractive semigroups and two-dimensional self-coupled Bose fields. J. Funct. Anal.9, 121–180 (1972)Google Scholar
  10. 10.
    Dixmier, J.: Les algèbres d'opérateurs dans l'espase hilbertien (Algèbres de von Neumann). Paris: Gauthier-Villars 1957Google Scholar
  11. 11.
    Glimm, J., Jaffe, A.: Energy-momentum spectrum and vacuum expectation values in quantum field theory. J. Math. Phys.11, 3335–3338 (1970)Google Scholar
  12. 12.
    McBryan, O. A.: Self-adjointness of relatively bounded quadratic forms and operators. J. Func. Anal.19, 97–103 (1975)Google Scholar
  13. 13.
    Glimm, J., Jaffe, A.: The λϕ24 quantum field theory without cutoffs. IV. Perturbations of the Hamiltonian. J. Math. Phys.13, 1568–1584 (1972)Google Scholar
  14. 14.
    Heifets, E., Osipov, E.: The energy-momentum spectrum in theP(ϕ)2 quantum field theory. Commun. math. Phys.56, 161–172 (1977)Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Edward P. Heifets
    • 1
  • Edward P. Osipov
    • 1
  1. 1.Department of Theoretical PhysicsInstitute for MathematicsNovosibirsk, 90USSR

Personalised recommendations