Current commutators at small time differences

  • I. Farkas
  • G. Pócsik


Using the equal-time current algebra and the divergence conditions, we calculate the current commutators for small time differences. It is shown that the commutators are explicitly model-dependent and the contributions of the symmetry-breaking terms do not drop out. The physical content of the current commutators of non-equal time is discussed in terms of new sum rules. We point out that the disconnected contributions are necessary for the consistency of the sum rules. The sum rules favour the field algebra.


Current Algebra Pole Approximation Rector Current Current Commutator Field Algebra 
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Коммутаторы тока при малых интервалах времени


Используя алгебру токов при равенстве времен, и условия расходимости, рассчитаны коммутаторы тока для малых интервалов времени. Показано, что коммутаторы явно зависят от модели, и вклады от членов, нарушающих симметрию не отнадают. Рассмотрено физическое содержание коммутаторов тока в терминах новых правил сумм. Показано, что для последовательности правил сумм необходимо наличие вкладов несвязанных диаграмм. Правила сумм дают предпочтение алгебре поля.


  1. 1.
    H. Leutwyler, Acta Phys. Austriaca, Suppl. V., 320, 1968.Google Scholar
  2. 2.
    J. Jersak andJ. Stern, Nuovo Cimento,59A, 315, 1969.ADSGoogle Scholar
  3. 3.
    S. Okubo, Physics,3, 165, 1967.MathSciNetGoogle Scholar
  4. 4.
    R. A. Brandt, Phys. Rev. Letters,23, 1260, 1969.CrossRefADSGoogle Scholar
  5. 5.
    R. L. Ingraham, Preprint, March, 1970.Google Scholar
  6. 6.
    Metric: + − − −Google Scholar
  7. 7.
    M. Gell-Mann, R. J. Oakes andB. Renner, Phys. Rev.,175, 2195, 1968.CrossRefADSGoogle Scholar
  8. 8.
    From the work ofF. Csikor andG. Pócsik, Nuovo Cimento,42A, 413, 1966, one concludes\(\left\langle {0\left| {\left[ {d^a \left( {\bar x,y_0 } \right)j_k^a \left( y \right)} \right]} \right|0} \right\rangle = 0\). The same result follows from the work ofS. Okubo Nuovo Cimento,43A, 1015, 1966 andD. Boulware andS. Deser, Phys. Rev.,151, 1278, 1966.ADSGoogle Scholar
  9. 9.
    \(\left\langle {0\left| {\left[ {\partial _0 d^a \left( {\bar x,y_0 } \right)j_0^a \left( y \right)} \right]} \right|0} \right\rangle = 0\) see [8]Google Scholar
  10. 10.
    S. Fubini andG. Furlan, Physics,1, 229, 1965.Google Scholar
  11. 11.
    D. Amati, R. Jengo andE. Remiddi, Nuovo Cimento,51A, 999, 1967.ADSGoogle Scholar
  12. 12.
    S. Fubini, Nuovo Cimento,43, 475, 1966.CrossRefADSGoogle Scholar
  13. 13.
    Similar conclusion has been reached in pole approximation byI. Montvay, Acta Phys. Hung.,25, 407, 1968.CrossRefGoogle Scholar
  14. 14.
    An application for the second time derivative of the chirality operator is treated byI. Farkas andG. Pócsik, ITP-Budapest Report No. 279, June 1970.Google Scholar

Copyright information

© with the authors 1972

Authors and Affiliations

  • I. Farkas
    • 1
  • G. Pócsik
    • 1
  1. 1.Institute for Theoretical PhysicsRoland Eötvös UniversityBudapest

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