Cohomological obstructions in locally variational field theories

21st International Conference on Integrable Systems and Quantum Symmetries

Francaviglia, Mauro^1 ; Palese, Marcella^1 ; Winterroth, Ekkehart^1

Department of Mathematics, University of Torino, via C. A.lberto 10, I-10124 Torino, Italy^1

关键词: Cohomology;    Conserved quantity;    Existence of global solution;    Field theory;    Global solutions;    Variational problems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012017/pdf
DOI  :  10.1088/1742-6596/474/1/012017

来源: IOP

【 摘 要 】

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.