Extended Hamiltonian formalism of field theories: variational aspects and other topics.

*(English)* Zbl 1210.70025
Mladenov, Ivaïlo (ed.) et al., Proceedings of the 7th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 2–10, 2005. Sofia: Bulgarian Academy of Sciences (ISBN 954-8495-30-9/pbk). 116-127 (2006).

Summary: We consider Hamiltonian systems in first-order multisymplectic field theories. In particular, we introduce Hamiltonian systems in the extended multimomentum bundle. The resulting extended Hamiltonian formalism is the generalization to field theories of the extended (symplectic) formalism for non-autonomous mechanical systems. In order to derive the corresponding field equations, a variational principle is stated for these extended Hamiltonian systems and, after studying the geometric properties of these systems, we establish the relation between this extended formalism and the standard one.

##### MSC:

70S05 | Lagrangian formalism and Hamiltonian formalism |

58E30 | Variational principles on infinite-dimensional spaces |

70G45 | Differential-geometric methods for dynamical systems |