Judith Arms | University of Washington (original) (raw)
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Papers by Judith Arms
Contemporary mathematics, 1988
Mathematical Sciences Research Institute publications, 1991
Letters in Mathematical Physics, 1979
Journal of Mathematical Physics, Apr 1, 1977
We obtain conditions on a compact Cauchy surface sufficient to insure linearization stability of ... more We obtain conditions on a compact Cauchy surface sufficient to insure linearization stability of the coupled Einstein–Maxwell equations, and identify these conditions with the absence of globally defined infinitesimal symmetries of the fields. The appropriate domain for these symmetries is a circle bundle over spacetime. The vector potential of the electromagnetic field is identified with the connection on the bundle.
Mathematical proceedings of the Cambridge Philosophical Society, Sep 1, 1981
Annals of Physics, Nov 1, 1982
Communications in Mathematical Physics, 1981
Birkhäuser Boston eBooks, 1991
Advances in Mathematics, 1990
General Relativity and Gravitation, Aug 1, 1977
![Research paper thumbnail of Erratum: Linearization stability and a globally singular change of variables [J. Math. Phys. <b>2</b> <b>1</b>, 15 (1980)]](https://attachments.academia-assets.com/115519263/thumbnails/1.jpg)
](Journal of Mathematical Physics, Jun 1, 1980
Nuclear physics, Mar 1, 1989
Journal of Geometry and Physics, Dec 1, 1996
Abstract A reduction of a Poisson manifold using the ideal I ( J ) generated by the momentum map ... more Abstract A reduction of a Poisson manifold using the ideal I ( J ) generated by the momentum map was introduced by Śniatycki and Weinstein (1983). This reduction has been extended to nonzero momentum values μ by two methods: by shifting to zero momentum on a larger space, the product with the coadjoint orbit; and by the method of Wilbour and Kimura (1991, 1993) using the modified ideal I ( J − μ ). It is shown that these two methods produce isomorphic reduced algebras under the assumptions that the symmetry group is connected and that the stabilizer group of μ also is connected. If the latter assumption fails, the shifted reduced algebra is isomorphic to a (possibly proper) subalgebra of the Wilbour-Kimura algebra.
Advances in Mathematics, 1990
Abstract. The zero set of a momentum mapping is shown to have a singularity at each point with sy... more 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. 1.
Indiana University Mathematics Journal, 1979
Contemporary mathematics, 1988
Mathematical Sciences Research Institute publications, 1991
Letters in Mathematical Physics, 1979
Journal of Mathematical Physics, Apr 1, 1977
We obtain conditions on a compact Cauchy surface sufficient to insure linearization stability of ... more We obtain conditions on a compact Cauchy surface sufficient to insure linearization stability of the coupled Einstein–Maxwell equations, and identify these conditions with the absence of globally defined infinitesimal symmetries of the fields. The appropriate domain for these symmetries is a circle bundle over spacetime. The vector potential of the electromagnetic field is identified with the connection on the bundle.
Mathematical proceedings of the Cambridge Philosophical Society, Sep 1, 1981
Annals of Physics, Nov 1, 1982
Communications in Mathematical Physics, 1981
Birkhäuser Boston eBooks, 1991
Advances in Mathematics, 1990
General Relativity and Gravitation, Aug 1, 1977
Journal of Mathematical Physics, Jun 1, 1980
Nuclear physics, Mar 1, 1989
Journal of Geometry and Physics, Dec 1, 1996
Abstract A reduction of a Poisson manifold using the ideal I ( J ) generated by the momentum map ... more Abstract A reduction of a Poisson manifold using the ideal I ( J ) generated by the momentum map was introduced by Śniatycki and Weinstein (1983). This reduction has been extended to nonzero momentum values μ by two methods: by shifting to zero momentum on a larger space, the product with the coadjoint orbit; and by the method of Wilbour and Kimura (1991, 1993) using the modified ideal I ( J − μ ). It is shown that these two methods produce isomorphic reduced algebras under the assumptions that the symmetry group is connected and that the stabilizer group of μ also is connected. If the latter assumption fails, the shifted reduced algebra is isomorphic to a (possibly proper) subalgebra of the Wilbour-Kimura algebra.
Advances in Mathematics, 1990
Abstract. The zero set of a momentum mapping is shown to have a singularity at each point with sy... more 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. 1.
Indiana University Mathematics Journal, 1979