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Algebraic study of chiral anomalies

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Abstract

The algebraic structure of chiral anomalies ismade globally valid on non-trivial bundles by the introduction of a fixed background connection. Some of the techniques used in the study of the anomaly are improved or generalized, including a systematic way of generating towers of ‘descent equations’.

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References

  1. R Jackiw, Topological investigations of quantized gauge theories, in: Relativ ity groups and topology II, Les Houches Lectures 1983, edited by B S De Witt and R Stora (North-Holland, Amsterdam, 1984)

  2. J Wess and B Zumino, Phys. Lett. B37, 95 (1971)

    MathSciNet  ADS  Google Scholar 

  3. C Becchi, A Rouet and R Stora, Ann. Phys. 98, 287 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  4. C Becchi, A Rouet and R Stora, Gauge field models, and renormalizable models with broken symmetries, in: Renormalization theory, Erice Lectures 1975, edited by G Velo and A S Wightman, NATO ASI Series C23 (Reidel, Dordrecht, 1976)

  5. C Becchi, A Rouet and R Stora, Renormalizable theories with symmetry breaking, in: Field theory quantization and statistical physics edited by E Tirapegui (Reidel, Dordrecht, 1981)

    Google Scholar 

  6. R Stora, Continuum gauge theories, in: New dev elopments in quantum field theory and statistical mechanics, 1976 Cargèse Lectures, edited by M Levy and P Mitter (Plenum Press, New York, 1977)

  7. E Witten, Nucl. Phys. B223, 422 (1983) L Alvarez-Gaumé and E Witten, Nucl. Phys. B234, 269 (1984)

  8. P Frampton, Phys. Lett. B122, 351 (1983) P Frampton and T Kephart, Phys. Rev . Lett. 50, 1343 (1983)

  9. B Zumino, Y S Wu and A Zee, Nucl. Phys. B239, 477 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  10. L Bonora and P Pasti, Phys. Lett. B132, 75 (1983)

    ADS  Google Scholar 

  11. B Zumino, Chiral anomalies and differential geometry, in: Relativ ity, groups and topology II, Les Houches Lectures 1983, edited by B S De Witt and R Stora (North-Holland, Amsterdam, 1984)

  12. R Stora, Algebraic structure and topological origin of anomalies, in: Recent progress in gauge theories, Cargèse Lectures 1983, edited by H Lehmann, NATO ASI Series (Plenum Press, New York, 1984)

  13. W A Bardeen and B Zumino, Nucl. Phys. B244, 421 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  14. M F Atiyah and I M Singer, Proc. Natl. Acad. Sci. USA 81, 2597 (1984)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. O Alvarez, I M Singer and B Zumino, Commun. Math. Phys. 96, 409 (1984)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. L Alvarez-Gaumé and P Ginsparg, Nucl. Phys. B243, 449 (1984); Ann. Phys. 161, 423 (1985)

  17. C Gómez, On the origin of non-Abelian anomalies (University of Salamanca), preprint DFTUS 06/83

  18. G C Rossi, M Testa and K Yoshida, Phys. Lett. B134, 78 (1984)

    ADS  Google Scholar 

  19. L Bonora and P Cotta-Ramusino, Commun. Math. Phys. 87, 589 (1983)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. F Langouche, T Schücker and R Stora, Phys. Lett. B145, 342 (1984)

    ADS  Google Scholar 

  21. L Baulieu and J Thierry-Mieg, Phys. Lett. B145, 53 (1984)

    MathSciNet  ADS  Google Scholar 

  22. C H Chang, H Y Guo, K Wu and X Song, Phys. Lett. B134, 67 (1984)

    ADS  Google Scholar 

  23. Ö Kaymakcalan, S Rajeev and J Schechter, Phys. Rev . D30, 594 (1984), SU-4222-278, COO-3533-278

  24. J Mañes, Nucl. Phys. B250, 369 (1985)

    Article  ADS  Google Scholar 

  25. H Kawai and S H H Tye, Phys. Lett. B140, 403 (1984)

    ADS  Google Scholar 

  26. R Ingermanson, Nucl. Phys. B249, 611 (1985)

    Article  ADS  Google Scholar 

  27. D Sullivan, IHES Publ. 47, 269 (1977)

    MATH  Google Scholar 

  28. A Guichardet, Cohomologie des groupes topologiques et algebres de Lie, CEDIC (Fernand Nathan, Paris, 1980)

  29. H Y Guo, K Wu and S K Wang, Commun. Theor. Phys. 4, 113 (1985)

    MathSciNet  Google Scholar 

  30. A G Reiman, L D Faddeev and M A Semenov, J. Funct. Anal. Appl. (in Russian) (1984)

  31. L D Faddeev, Phys. Lett. B145, 81 (1984)

    MathSciNet  ADS  Google Scholar 

  32. B Zumino, Nucl. Phys. B253, 477 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  33. Y S Wu, Phys. Lett. B153, 70 (1985)

    ADS  Google Scholar 

  34. H Y Guo, B Y Hou, S K Wang and K Wu, Commun. Theor. Phys. 4, 145 (1985)

    MathSciNet  Google Scholar 

  35. W A Bardeen, Phys. Rev . 184, 1848 (1969)

    Article  ADS  Google Scholar 

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Correspondence to BRUNO ZUMINO.

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Editor’s Note:

 Reproduced with kind permission from Springer Science+Business Media: Algebraic study of chiral anomalies, Juan Mañes, Raymond Stora and Bruno Zumino, Communications in Mathematical Physics 102, 157–174 (1985) Springer-Verlag. Even though at variance with normal Pramana policy, we are proud to reproduce this article of exceptional quality and lasting scientific value. It marks a milestone in the joint work of Raymond Stora and B Zumino, addressing issues on symmetries in gauge theories.

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MAÑES, J., STORA, R. & ZUMINO, B. Algebraic study of chiral anomalies . Pramana - J Phys 78, 907–925 (2012). https://doi.org/10.1007/s12043-012-0316-3

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