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Communications in Mathematical Physics

, Volume 8, Issue 4, pp 327–337 | Cite as

On equal-time commutation relations of renormalized currents in perturbation theory I

  • B. Schroer
  • P. Stichel
Article

Abstract

Equal-time current commutation relations are considered in renormalizable field theories. Renormalized currents are obtained by means of solutions of the Yang-Feldman equations for Heisenberg field operators in perturbation theory. For the computation of matrix elements of current commutators we apply Jost-Lehmann-Dyson type techniques. The equal time limit is taken with the help of symmetrical time-smearing functions which interpolate the δ-function. Our methods avoid any cut-off procedure and lead therefore to unambiguous results. In order to avoid spin complications, our general methods are applied to trilinear resp. quadrilinear couplings of isoscalar and isovector spin 0-mesons in first order perturbation theory. We find that the zero-space components of the current-commutator matrix elements behave for small time separationT like ln(T) grad x δ(X–Y).

Keywords

Matrix Element Perturbation Theory Commutation Relation Order Perturbation Order Perturbation Theory 
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.

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References

  1. 1.
    Schroer, B., andP. Stichel: Commun. Math. Phys.3, 258 (1966).Google Scholar
  2. 2.
    Johnson, K., andF. E. Low: Progr. Theor. Phys. Suppl.37, 38, 74 (1966).Google Scholar
  3. 3.
    Hamprecht, B.: Nuovo Cimento47 A, 770 (1967) and50A, 449 (1967). —Polkinghorne, J. C.: Nuovo Cimento52A, 351 (1967). We do not quote papers, where primarily sum rules and not ETCR are checked in perturbation theory.Google Scholar
  4. 4.
    Langerholc, J.: DESY 67/26, August 1967.Google Scholar
  5. 5.
    Kuo, T. K., andM. Sugawara: Phys. Rev.151, 1181 (1966).Google Scholar
  6. 6.
    Adler, S. L., andC. G. Callan: CERN, TH. 587 (1965). —Kramer, G., andK. Meetz: DESY 67/11, April 1967.Google Scholar
  7. 7.
    Gell-Mann, M.: Phys. Rev.125, 1067 (1962).Google Scholar
  8. 8.
    Adler, S. L., andC. G. Callan: CERN, TH. 587 (1965).Google Scholar
  9. 9.
    Gell-Mann, M., andM. Levy: Nuovo Cimento16, 705 (1960).Google Scholar
  10. 10.
    Compare chapter VI inG. Källen's review article on Quantum Electrodynamics in: Encyclopedia of Physics, Vol. V, Part 1. Berlin-Göttingen-Heidelberg: Springer 1958.Google Scholar
  11. 11.
    Compare:Kramer, G., andK. Meetz: Commun. Math. Phys.3, 29 (1966).Google Scholar

Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • B. Schroer
    • 1
  • P. Stichel
    • 2
    • 3
  1. 1.University of PittsburghPittsburgh 13
  2. 2.Deutsches Elektronen-Synchrotron (DESY)Hamburg
  3. 3.Physikalisches Staatsinstitut II. Inst. f. ExperimentalphysikHamburg 50

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