Authors: Jordi Gaset ; Pedro D. Prieto-Martínez ; Narciso Román-Roy

The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multi-symplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous) mechanics.

• 49S05 - Variational principles of physics
• 55R10 - Fiber bundles in algebraic topology
• 58E30 - Variational principles in infinite-dimensional spaces
• 70S10 - Symmetries and conservation laws in mechanics of particles and systems