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


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).


Matrix Element Perturbation Theory Commutation Relation Order Perturbation Order Perturbation Theory 
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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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