Mathematical Sciences: RUI: A Multisymplectic Approach to Classical Field Theory

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This research is concerned with the mathematical foundations of classical field theory. The work will develop a covariant Hamiltonian formalism in the calculus of variations which will provide a general and systematic means of analyzing any variational principle. The key ingredient in this work is a generalization of the notion of a multisymplectic structure. This work should furnish a comprehensive basis for studying questions related to symmetries, the Cauchy problem, linearization, stability, and quantization.