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Poisson brackets between two super-Hamiltonians on canonical coordinates (spatial metrics in geometrodynamics and embedding variables in parametrized theories) is usually regarded as an indication that the Dirac relations cannot be connected with a representation of the complete Lie algebra L Diffd of spacetime diffeomorphisms. It is shown how this difficulty may be overcome and a homomorphic mapping of spacetime vector fields YE L Diff 4 into the Poisson bracket algebra on the phase space of the system constructed. How the technique works in the case of a parametrized field theory is explained in the present paper, and it is generalized to canonical geometrodynamics in the companion paper (Part II). In a parametrized theory, the phase space of the system is the ordinary phase space of the field augmented by the embedding variables X: I --t 4 and their conjugate momenta. The dynamical variable H( I') which represents YE L Diff & generates a deformation of the embedding along the flow lines of Y accompanied by the correct dynamical evolution of the held data and preserves the constraints in the extended phase space of the system. The relation between the representations of Diff z and Diff A is also established.
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The detailed account of analytic calculation of radiative-recoil corrections to muonium hyperline splitting, induced by electron-line radiative insertions, is presented. The consideration is performed in the framework of the effective two-particle formalism. A good deal of attention is paid to the p