Multisymplectic Formalism for Cubic Horndeski Theories

TL;DR

This paper develops a covariant multisymplectic framework for cubic Horndeski theories, clarifying the geometric structure and constraints, and exploring conditions for a simplified Hamiltonian formulation.

Contribution

It introduces a covariant multisymplectic formalism for cubic Horndeski theories and analyzes the conditions for projecting the Lagrangian to the Hamiltonian formalism.

Findings

Identifies conditions for the Poincaré-Cartan form to project onto $J^1oldsymbol{ ho}$

Explores when a formulation using only multimomenta is feasible

Discusses implications when projection conditions are not satisfied

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 $J^1\pi$. 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 $J^1\pi$ conditions are not met.