More Insights into Symmetries in Multisymplectic Field Theories

Abstract

This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics and in the geometric formulation of these theories are clarified. Finally, a general discussion is given on the structure of symmetries in the presence of constraints appearing in singular field theories. Symmetries of some typical theories in theoretical physics are analyzed through the construction of the relevant multimomentum maps which are the conserved quantities (by Noether’s theorem) on the (pre)multisymplectic phase spaces.

Keywords

• Lagrangian and Hamiltonian field theories
• jet bundles
• multisymplectic forms
• symmetries
• noether symmetries
• gauge symmetries