Descendants of the Chiral Anomaly

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Jackiw, R.;
  • Subject: Mathematical Physics | High Energy Physics - Theory
    arxiv: Mathematics::K-Theory and Homology | High Energy Physics::Theory

Chern-Simons terms are well-known descendants of chiral anomalies, when the latter are presented as total derivatives. Here I explain that also Chern-Simons terms, when defined on a 3-manifold, may be expressed as total derivatives.
  • References (8)

    [1] S. Deser, R. Jackiw and S. Templeton, “Topologically Massive Gauge Theories”, Ann. Phys. (NY) 149, 372 (1982), (E) 185, 406 (1985).

    [2] Fluid mechanics and magnetohydrodynamics were the contexts in which the Abelian Chern-Simons term made its first appearance: L. Woltier, “A Theorem on Force-Free Magnetic Fields”, Proc. Nat. Acad. Sci. 44, 489 (1958).

    [3] S. Deser, “Relations Between Mathematics and Physics”, IHES Publications in Mathematics , 1847 (1998), “Physicomathematical Interaction: The Chern-Simons Story”, Faddeev Festschrift, Proc. V.A. Steklov Inst. Math. 226, 180 (1999).

    [4] For a review, see R. Jackiw, “(A Particle Field Theorist's) Lectures on (Supersymmetric, Non-Abelian) Fluid Mechanics (and d-Branes)”, e-print: physics/0010042.

    [5] For a review, see H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge UK 1932), p. 248 and Ref. [4].

    [6] A constructive discussion of the Darboux theorem is by R. Jackiw, “(Constrained) Quantization without Tears”, in Constraint Theory and Quantization Methods, F. Colomo, L. Lusann, and G. Marmo, eds. (World Scientific, Singapore 1994), reprinted in R. Jackiw, Diverse Topics in Theoretical and Mathematical Physics (World Scientific, Singapore 1996).

    [7] R. Jackiw and S.-Y. Pi, “Creation and Evolution of Magnetic Helicity”, Phys. Rev. D 61, 105015 (2000).

    [8] R. Jackiw, V.P. Nair, and S.-Y. Pi, “Chern-Simons Reduction and Non-Abelian Fluid Mechanics”, Phys. Rev. D 62, 085018 (2000).

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