Presymplectic structures and intrinsic Lagrangians for massive fields

Understand

We study the construction of the so-called intrinsic action for PDEs equipped with compatible presymplectic structures.

• In particular, we explicitly demonstrate that the intrinsic action for the standard Einstein-Hilbert gravity is the familiar first-order Palatini action.
• Our main focus in this work is the massive spin-2 field, where the natural presymplectic structure is not complete in the sense that the associated intrinsic action does not reproduce all the equations of motion.
• We explicitly relate this feature to the differential consequences of the zeroth order in the genuine Lagrangian formulation of Fierz and Pauli.