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Quantum Mechanics of Fundamental Systems 1 pp 145–165Cite as

Update on Anomalous Theories

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Abstract

It is known that the. quantization procedure can spoil classical symmetries. The problem afflicts continuous chiral symmetries and gravitational symmetries of massless (Weyl) fermions, the former in any even-dimensional space-time, the latter in space-times with dimensionality 4k + 2, k = 0,1,.... [Similar quantum breaking afflicts discrete symmetries (P, T) in odd dimensions, and scale/conformai symmetries in any dimension; we shall not be concerned with these.] As a consequence, the symmetry current, whose classical conservation is assured by Noether’s theorem, ceases to be conserved after quantization. We call such a current anomalous; it possesses an anomalous divergence, and the coupling of gauge fields to this current becomes problematical [1].

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References AND Notes

  1. For a review and references to the original literature, see S. Treiman, R. Jackiw, B. Zumino, and E. Witten, Current Algebra and Anomalies, Princeton University Press, Princeton, New Jersey/World Scientific, Singapore, 1985;

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  2. For a review and references to the original literature, see S. Treiman, R. Jackiw, B. Zumino, and E. Witten, Anomalies, Geometry, Topology (W. Bardeen and A. White, eds.), World Scientific, Singapore, 1985.

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  49. E. D’Hoker and E. Farhi, in unpublished research, have convinced themselves that their model (Ref. 9), with a kinetic term for the Wess-Zumino chiral field, is not renormalizable.

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  1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA

    R. Jackiw

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Editors and Affiliations

  1. Centro de Estudios Científicos de Santiago, Santiago, Chile

    Claudio Teitelboim

  2. University of Texas at Austin, Austin, Texas, USA

    Claudio Teitelboim

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Jackiw, R. (1988). Update on Anomalous Theories. In: Teitelboim, C. (eds) Quantum Mechanics of Fundamental Systems 1. Series of the Centro de Estudios Científicos de Santiago. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3728-5_11

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  • DOI: https://doi.org/10.1007/978-1-4899-3728-5_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-3730-8

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