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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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.
|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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