Anomalous current commutators in the nonlinear <i>σ</i> model

G. Kramer; WIlliam F. Palmer

doi:10.1103/PhysRevD.33.1505

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Anomalous current commutators in the nonlinear σ model

G. Kramer

WIlliam F. Palmer

II. Institut für Theoretische Physik der Universitat Hamburg, 2 Hamburg 50, Federal Republic of Germany

Department of Physics, Ohio State University, Columbus, Ohio 43210

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Phys. Rev. D 33, 1505 – Published 1 March, 1986

DOI: https://doi.org/10.1103/PhysRevD.33.1505

Abstract

We calculate the equal-time commutation relations of the chiral SU(3 $)_{L}$ ×SU(3 $)_{R}$ charge densities in the nonlinear σ model and obtain operator-valued Schwinger-term modifications arising from the axial anomaly. We check the modified commutators by a current-algebra derivation of the anomalous matrix element 〈 $π^{+}$ $π^{-}$ $π^{0}$ ‖ $V_{0}^{8}$ ‖0〉. The result agrees with that obtained directly from the Wess-Zumino effective Lagrangian.

References (7)

S. L. Adler, Phys. Rev. 177, 2426 (1969); J. S. Bell and R. Jackiw, Nuovo Cimento 60, 147 (1969); W. A. Bardeen, Phys. Rev. 184, 1848 (1969).
J. Wess and B. Zumino, Phys. Lett. 37B, 95 (1971).
E. Witten, Nucl. Phys. B223, 422 (1983).
G. Kramer, W. Palmer and S. Pinsky, Phys. Rev. D 30, 89 (1984). We would like to point out that this reference has the wrong sign in the normal parts of the right- and left-handed currents.
I. Bars, in Proceedings of the Conference on Vertex Operators in Mathematics and Physics, Berkeley, California, 1983, edited by J. Lepowsky, S. Mandelstam, and I. M. Singer (Springer, New York, 1985), p. 373.
S. Rajeev, Phys. Rev. D 29, 2944 (1984).
S.-C. Chao, G. Kramer, W. Palmer and S. Pinsky, Phys. Rev. D 30, 1916 (1984).

[c1] S. L. Adler, Phys. Rev. 177, 2426 (1969); J. S. Bell and R. Jackiw, Nuovo Cimento 60, 147 (1969); W. A. Bardeen, Phys. Rev. 184, 1848 (1969).

[c2] J. Wess and B. Zumino, Phys. Lett. 37B, 95 (1971).

[c3] E. Witten, Nucl. Phys. B223, 422 (1983).

[c4] G. Kramer, W. Palmer and S. Pinsky, Phys. Rev. D 30, 89 (1984). We would like to point out that this reference has the wrong sign in the normal parts of the right- and left-handed currents.

[c5] I. Bars, in Proceedings of the Conference on Vertex Operators in Mathematics and Physics, Berkeley, California, 1983, edited by J. Lepowsky, S. Mandelstam, and I. M. Singer (Springer, New York, 1985), p. 373.

[c6] S. Rajeev, Phys. Rev. D 29, 2944 (1984).

[c7] S.-C. Chao, G. Kramer, W. Palmer and S. Pinsky, Phys. Rev. D 30, 1916 (1984).

Physical Review D

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Anomalous current commutators in the nonlinear σ model

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References (7)

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