SYMMETRIC AND ASYMMETRIC ANOMALIES AND EFFECTIVE LAGRANGIAN

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Communications in Theoretical Physics ›› 1984, Vol. 3 ›› Issue (5) : 593-603.

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SYMMETRIC AND ASYMMETRIC ANOMALIES AND EFFECTIVE LAGRANGIAN

Kuang-chao CHO¹, Han-ying GUO²

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Abstract

The properties of the effective Lagrangian for the low-energy Goldstone-gauge field system constructed from the Chern-Simons topological invariant are further discussed. Both the symmetric anomaly and the asymmetric anomaly are connected with this Lagrangian.

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Kuang-chao CHO, Han-ying GUO, Ke WU, Xing-Chang SONG. SYMMETRIC AND ASYMMETRIC ANOMALIES AND EFFECTIVE LAGRANGIAN[J]. Communications in Theoretical Physics, 1984, 3(5): 593-603

References

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

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

[3] K.C. CHOU, H.Y. GUO. K. WU and X.C. SONG, PhyS. Lett. 134B(1984)67.

[4] K.C. CHOU, H.Y. GUO, K. WU and X.C. SONG, Commun. in Theor. phys. 3(1984)73.

[5] Here we mean the result presented in the Appendix of Ref.

[4] , which i s obtained by correcting some misprints and adding some missed terms. It produces correct anomalies and takes the form nearest to the original one in Eq.(24)of Ref.

[1] .

[6] W.A. Bardeen, Phys. Rep. 184(1969)1848; R. W. Brown, C.C. Shih, and B.L. Young, Phys. Rev. 186(1969)1491.

[7] D.J. Gross and R. Jackiw, Phys. Rev. D6(1972)477.

[8] The fact that the infinitesimal variation of the Chern-Simons 5-form gives correct anomalies has been independently noticed by B. Zumino, Y.S. Wu and A. Zee, university of Washington preprint 40048-17, to be published in Nucl. Phys. See also B. Zumino, lectures given a t Les Houches, LBL-16746, Aug.1983.

[9] See R. Jackiw, Lecture given at Les Houches, MIT preprint CTP #1108, Aug. 1983. For original discussion about equation of motion and conservation law in anomalous case, see S. Adler in Lectureson Elementary Particles and Quantum Field Theory, edited by S. Deser, M. Grisaru and H. Pendleton (MIT Press, Cambridge, MA 1970).

[10] O. Kaymakcalan, S. Rajeev and J. Schechter, Syracuse preprint su-4222-278, Dec. 1983.

[ll] H. Kawai and S.H.H. Tye, Cornell preprint CLNS-84/595, Jan. 1984.