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The Rôle of Stratification in Anomalies

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Geometry and Theoretical Physics
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Abstract

The relation between symmetries and anomalies is discussed, with particular emphasis on the rôle of the group action. The action of the full gauge group on the space of gauge potentials is investigated in connection with chiral anomalies in gauge theories. This allows the treatment of all gauge anomalies within the framework of the Atiyah-Singer Index Theorems.

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References

  1. J. Steinberger: Phys. Rev. 76, 1180 (1949)

    Article  ADS  MATH  Google Scholar 

  2. S.L. Adler: Phys. Rev. 177, 2426 (1969); J.S. Bell and R. Jackiw: Nuovo Cimento A60, 47 (1969); W.A. Bardeen: Phys. Rev. 184, 1848 (1969)

    Article  Google Scholar 

  3. H. Römer: In Differential Geometric Methods in Theoretical Physics, ed. by H.D. Doebner, Lecture Notes in Physics 139 (Springer, Berlin, Heidelberg 1978); R. Stora: In Non-Perturbative Methods, ed. by S. Narrison (World Scientific, Singapore 1985); B. Zumino: In Relativity, Groups and Topology II, Les Houches (North Holland, Amsterdam 1983); H. Leutwyler: In The Fundamental Interaction, ed. by J. Debrus and A.C. Hirshfeld ( Plenum Press, New York, London 1988 )

    Google Scholar 

  4. M.F. Atiyah and I.M. Singer: Proc. Nat. Acad. Sci. USA 81, 2597 (1984); I. M. Singer: Société Mathématique de Prance, Astérisque 323 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  5. L.D. Faddeev and S.L. Shatashvili: Theor. Math. Phys. 60, 770 (1985); K. Fujikawa: Phys. Rev. D21, 2848 (1980); A.Yu. Morozov: Sov. Phys. Usp. Zg. 11 (1986); J. Sidenius: preprint NORDITA-85/33; L. Alvarez-Gaume: preprint HUTP-85/A092

    Article  Google Scholar 

  6. D. Kastler and R. Stora: preprint CPT-86 (1985); M. Dubois-Violette: preprint Orsay LPTHE-86-12; L. Bonora, P. Cotta-Ramusino, M. Rinaldi and J. Stasheff: Comm. Math. Phys. 112, 237 (1987); Comm. Math. Phys. 114, 381 (1988)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. A. Heil, N.A. Papadopoulos, B. Reifenhäuser and F. Scheck: Nucl. Phys. B293, 445 (1987); A. Heil, A. Kersch, N;A. Papadopoulos, B. Reifenhäuser, F. Scheck and H. Vogel: Jour. Geom. Phys. 6.2, 237 (1989); F. Scheck: “Geometrical Approaches to Particle Physics”, Mainz preprint (1990)

    Article  ADS  Google Scholar 

  8. A. Heil, A. Kersch, N.A. Papadopoulos, B. Reifenhäuser and F. Scheck: Ann. Phys. (New York) 206, 200 (1990)

    Google Scholar 

  9. A. Heil, A. Kersch, N.A. Papadopoulos, B. Reifenhäuser and F. Scheck: “Structure of the space of reducible Yang-Mills potentials”, Mainz preprint (1990)

    Google Scholar 

  10. M.F. Atiyah and I.M. Singer: Ann. Math. 87, 484 (1968); Ann. Math. 87, 546 (1968); Ann. Math. 92, 139 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Kersch: “Anomalien im Rahmen des Indextheorems”, Diss. Mainz (1990)

    Google Scholar 

  12. E. Binz, J. Sniatycki and H. Fischer: Geometry of Classical Fields, North Holland Mathematics Studies 154 ( North Holland, Amsterdam 1988 )

    MATH  Google Scholar 

  13. M.F. Atiyah: Scuola Normale Superiore, Pisa (1979); Lecture Notes in Physics 208 (Springer, Berlin, Heidelberg 1984 )

    Google Scholar 

  14. G.E. Bredon: Introduction to Compact Transformation Groups ( Academic Press, New York 1972 );

    MATH  Google Scholar 

  15. K. Jänich, Lecture Notes in Mathematics 59 ( Springer, Berlin, Heidelberg 1968 )

    Google Scholar 

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© 1991 Springer-Verlag Berlin Heidelberg

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Papadopoulos, N.A. (1991). The Rôle of Stratification in Anomalies. In: Debrus, J., Hirshfeld, A.C. (eds) Geometry and Theoretical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76353-3_7

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  • DOI: https://doi.org/10.1007/978-3-642-76353-3_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-76355-7

  • Online ISBN: 978-3-642-76353-3

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