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Augmented variational principles and relative conservation laws in classical field theory. (English) Zbl 1133.70335

Augmented variational principles are introduced in order to provide a definition of relative conservation laws. As it is physically reasonable, relative conservation laws define in turn relative conserved quantities that measure, for example, how much energy is needed in a field theory to go from one configuration (called the reference or vacuum) to another configuration (the physical state of the system). The general prescription we describe solves in a covariant way the well-known observer dependence of conserved quantities. The solution found is deeply related to the divergence ambiguity of the Lagrangian and to various formalisms that have recently appeared in literature to deal with the variation of conserved quantities (of which this is a formal integration). A number of examples relevant to fundamental physics are considered in detail, starting from classical mechanics.

MSC:

70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
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References:

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