Multisymplectic formalism for cubic horndeski theories

Abstract

We present the covariant multisymplectic formalism for the so-called cubic Horndeski theories and discuss the geometrical and physical interpretation of the constraints that arise in the unified Lagrangian-Hamiltonian approach. We analyse in more detail the covariant Hamiltonian formalism of these theories and we show that there are particular conditions that must be satisfied for the Poincar´e-Cartan form of the Lagrangian to project onto J1π. From this result, we study when a formulation using only multimomenta is possible. We further discuss the implications of the general case, in which the projection onto J1π conditions are not met.