Local symmetries of the Einstein-Yang-Mills theory as phase-space transformations

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Abstract
For Einstein's theory of gravitation coupled to scalar and Yang-Mills sources we implement local symmetries as canonical transformations in a phase space. This is carried out without any action principle. The procedure allows one to rederive the supermomentum for the Einstein-scalar fields, and both the supermomentum and super-Hamiltonian of the coupled Einstein-Yang-Mills system. For the latter theory it turns out that general coordinate transformations alone cannot be realized in a phase space.