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Frame bundle
About: Frame bundle is a research topic. Over the lifetime, 1600 publications have been published within this topic receiving 23049 citations.
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TL;DR: In this article, it was shown that these two reduction procedures are, in an appropriate sense, equivalent for a class of field theories whose fields take values in a principal bundle, including examples such as a sea of rigid bodies with and appropriate interbody coupling potential.
Abstract: Reduction for field theories with symmetry can be done either covariantly—that is, on spacetime—or dynamically—that is, after spacetime is split into space and time. The purpose of this article is to show that these two reduction procedures are, in an appropriate sense, equivalent for a class of field theories whose fields take values in a principal bundle. One can think of this class of field theories as including examples such as a “sea of rigid bodies” with and appropriate interbody coupling potential.
16 citations
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16 citations
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16 citations
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01 Nov 2006
TL;DR: In this article, it was shown that the vector bundle structure on a smooth Banach manifold remains invariant under conjugate connections with respect to diffeomorphisms of the manifold.
Abstract: On a smooth Banach manifold M, the equivalence classes of curves that agree up to acceleration form the second order tangent bundle T^2M of M. This is a vector bundle in the presence of a linear connection on M and the corresponding local structure is heavily dependent on the choice of connection. In this paper we study the extent of this
dependence and we prove that it is closely related to the notions of conjugate connections and second order differentials. In particular, the vector bundle structure on T^2M remains invariant under conjugate connections with respect to diffeomorphisms of M.
16 citations