Hamilton formulation of a theory with high derivatives

Hamiltonization of theories with degenerate coordinates

“…A generalization of the definition (1) for theories with the Lagrange function L and orders {N a } was proposed in [5,2]. Such a definition is based on a simple generalization of the Hessian,…”

“…Thus, we arrive at the Hamilton action S H and at the Hamilton EM for unconstrained phase-space variables x a s , p [6]. The Hamiltonization of singular theories with higher-order time derivatives, on the base of the action (5), was considered in [5,2].…”

“…In particular, it depends on the highest orders of time derivatives in the Lagrange function. In principle, the Hamiltonization procedure is quite well developed for theories of arbitrary orders N ≥ 1 of time derivatives [5]. However, as we are going to demonstrate, for a class of theories where part of the coordinates does not have any time derivatives in the Lagrange function (we call such coordinates degenerate) it is reasonable to reconsider the conventional definition of singularity and, moreover, to simplify the conventional Hamiltonization procedure.…”

Multi-Hamiltonian formulations and stability of higher-derivative extensions of 3d Chern–Simons

“…In the other wording, changing values of parameters β, we simultaneously change Hamiltonian H T (β) and Poisson brackets {·, ·} β in such a way that the equations of motion (4) remain intact. Any higher-derivative Lagrangian field theory always admits at least one Hamiltonian formulation which can be constructed by the Ostrogradski method in the unconstrained case, and by various generalizations [27][28][29][30] developed for the constrained systems. In this paper, we develop the Hamiltonian formalism of higher-derivative field theory in several respects by the example of the model (3).…”

“…Its generalization for singular Lagrangians was first worked out in the paper [27]. The general constrained Hamiltonian formalism of higher-derivative systems was further developed since that in various directions.…”