Equivariance, variational principles, and the Feynman integral.
Svetlichny, George (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Svetlichny, George (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Krupka, D., Krupka, M. (2010)
Balkan Journal of Geometry and its Applications (BJGA)
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Mauro Francaviglia, M. Palese, E. Winterroth (2012)
Communications in Mathematics
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We introduce the concept of conserved current variationally associated with locally variational invariant field equations. The invariance of the variation of the corresponding local presentation is a sufficient condition for the current beeing variationally equivalent to a global one. The case of a Chern-Simons theory is worked out and a global current is variationally associated with a Chern-Simons local Lagrangian.
David Saunders (2010)
Communications in Mathematics
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This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.
Borowiec, A., Ferraris, M., Francaviglia, M., Palese, M. (2003)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Olga Rossi, Jana Musilová (2012)
Communications in Mathematics
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The inverse problem of the calculus of variations in a nonholonomic setting is studied. The concept of constraint variationality is introduced on the basis of a recently discovered nonholonomic variational principle. Variational properties of first order mechanical systems with general nonholonomic constraints are studied. It is shown that constraint variationality is equivalent with the existence of a closed representative in the class of 2-forms determining the nonholonomic system....