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Symmetry and Bifurcations of Momentum Mappings

Arms, Judith M. and Marsden, Jerrold E. and Moncrief, Vincent (1981) Symmetry and Bifurcations of Momentum Mappings. Communications in Mathematical Physics, 78 (4). pp. 455-478. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20100712-140837776

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Abstract

The zero set of a momentum mapping is shown to have a singularity at each point with symmetry. The zero set is diffeomorphic to the product of a manifold and the zero set of a homogeneous quadratic function. The proof uses the Kuranishi theory of deformations. Among the applications, it is shown that the set of all solutions of the Yang-Mills equations on a Lorentz manifold has a singularity at any solution with symmetry, in the sense of a pure gauge symmetry. Similarly, the set of solutions of Einstein's equations has a singularity at any solution that has spacelike Killing fields, provided the spacetime has a compact Cauchy surface.


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Additional Information:© Springer-Verlag 1981. Received January 31, 1980. This work was partially supported by the National Science Foundation. The second author was supported by a Killam Visiting fellowship at the University of Calgary during the completion of the paper. It is a pleasure to thank M. Berger, M. Buchner, Y. Choquet-Bruhat, A. Fischer, M. Gotay, R.Jackiw, L.Nirenberg, S. Schecter, I. Singer, J. Sniatycki, F. Tipler, W. Tulczyjew, and A. Weinstein for their interest in this work and their comments. Communicated by A. Jaffe
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Deposited By: Ruth Sustaita
Deposited On:13 Jul 2010 15:48
Last Modified:26 Dec 2012 12:13

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