Gauge-natural parameterized variational problems, vakonomic field theories and relativistic hydrodynamics of a charged fluid

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dc.creatorBibbona, Enrico
dc.creatorFatibene, Lorenzo
dc.creatorFrancaviglia, Mauro
dc.date2006-04-21
dc.date2006-04-26
dc.date.accessioned2026-07-07T07:40:55Z
dc.date.available2026-07-07T07:40:55Z
dc.descriptionVariational principles for field theories where variations of fields are restricted along a parametrization are considered. In particular, gauge-natural parametrized variational problems are defined as those in which both the Lagrangian and the parametrization are gauge covariant and some further conditions is satisfied in order to formulate a Nöther theorem that links horizontal and gauge symmetries to the relative conservation laws (generalizing what Fern{á}ndez, Garc{\'ı}a and Rodrigo did in some recent papers). The case of vakonomic constraints in field theory is also studied within the framework of parametrized variational problems, defining and comparing two different concepts of criticality of a section, one arising directly from the vakonomic schema, the other making use of an adapted parametrization. The general theory is then applied to the case of hydrodynamics of a charged fluid coupled with its gravitational and electromagnetic field. A variational formulation including conserved currents and superpotentials is given that turns out to be computationally much easier than the standard one.
dc.identifierhttps://arxiv.org/abs/math-ph/0604053
dc.identifierhttp://arxiv.org/abs/math-ph/0604053
dc.identifierInt.J.Geom.Meth.Mod.Phys. 3 (2006) 1573-1608
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121924
dc.subjectMathematical Physics
dc.subject70S05, 58E50, 83C40, 76M30
dc.titleGauge-natural parameterized variational problems, vakonomic field theories and relativistic hydrodynamics of a charged fluid
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