Symmetry Breaking and Sigma Commutators
In the context of broken chiral symmetry the sigma commutators, the evaluation of their matrix elements and the significance of the resulting magnitudes are discussed.
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SYMMETRY BREAKING AND SIGMA COMMUTATORS
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BY R. J. OAKES Department of Physics,Northwestern University Evanston, Illinois 6020l,U.S.A. and Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany
ABSTRACT In the context of broken chiral symmetry the sigma commutators, the evaluation of their matrix elements and the significance of the resulting magnitudes are discussed.
INTRODUCTION Recently there has been renewed interest in the old question of the chiral SU(3)xSU(3) sigma commutators and the magnitudes of their various matrix elements. In these two lectures I would like to review the recent contributions to our understanding of this problem, comparing the different approaches and discussing the implications of various results that have been obtained. For the sake of clarity :: Lecture given at XI. Internationale Universitatswochen fOr Kernphysik, Schladming, February 21 - March 4, 1972. ""supported in part by the National Science Foundation under Grant No. GP-25203.
519 and completeness a certain amount of background material has been included, also.
CHIRAL SU(3)xSU(3) SIGMA COMMUTATORS In the case of any approximate symmetry generated by the space-integrals of time-components of four-vector currents the question of how the divergences of the currents transform naturally arises. If the symmetry were exact the divergences of the currents would all vanish and the question would be trivial. However, in the more realistic case of approximate symmetries, such as chiral SU(3)xSU(3), where the currents themselves belong to the adjoint representation (1,8)+(8,1), the transformation properties of the current divergences are an important question to investigate since they depend on how the symmetry is broken. Taking the example of chiral SU(3)xSU(3) we have at equal times the charge-current commutators [ 1] [Q(a.) (t) ,
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