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Cohomological obstructions in locally variational field theories

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, , Citation Mauro Francaviglia et al 2013 J. Phys.: Conf. Ser. 474 012017 DOI 10.1088/1742-6596/474/1/012017

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1 Mauro Francaviglia suddenly passed away in June 2013; this paper is the outcome of our recent joint research work and we dedicate it to his memory

2 Department of Mathematics, University of Torino, via C. A.lberto 10, I-10124 Torino, Italy

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1742-6596/474/1/012017

Abstract

We study cohomological obstructions to the existence of global conserved quantities. In particular, we show that, if a given local variational problem is supposed to admit global solutions, certain cohomology classes cannot appear as obstructions. Vice versa, we obtain a new type of cohomological obstruction to the existence of global solutions for a variational problem.

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10.1088/1742-6596/474/1/012017