Modified Hamiltonian formalism for higher-derivative theories

Abstract

The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables yields proper equations of motion; no additional Lagrange multipliers are necessary (ii) the Legendre transformation can be performed in a straightforward way provided the Lagrangian is nonsingular in Ostrogradski sense. The generalization to singular Lagrangians as well as field theory are presented.

22 pages; no figures; some comments added; accepted for publication in Phys. Rev. D

References in corpus (5)

• f(R) theories
• Various Hamiltonian formulations of f(R) gravity and their canonical relationships
• Radiation Beyond Four Space-Time Dimensions
• Self-Interaction and Regularization of Classical Electrodynamics in Higher Dimensions
• On the Problem of Radiation Friction Beyond 4 and 6 Dimensions

Cited by in corpus (15)

• Third order equations of motion and the Ostrogradsky instability
• A Lagrangian constraint analysis of first order classical field theories with an application to gravity
• Gauge invariances of higher derivative Maxwell-Chern-Simons field theory -- a new Hamiltonian approach
• Eisenhart lift for higher derivative systems
• Nonrelativistic conformal transformations in Lagrangian formalism
• Hamiltonian analysis for linearly acceleration-dependent Lagrangians
• Complete Hamiltonian analysis of cosmological perturbations at all orders
• A Hamilton-Jacobi formalism for higher order implicit systems
• Isotropic universe with almost scale-invariant fourth-order gravity
• Reductions of Topologically Massive Gravity I: Hamiltonian Analysis of The Second Order Degenerate Lagrangians
• Non-trivial time crystal-like ground state for gravitational perturbation in quadratic gravity
• Hamiltonian formalism of cosmological perturbations and higher derivative theories
• Formulation of singular theories in a partial Hamiltonian formalism using a new bracket and multi-time dynamics
• Reductions of Topologically Massive Gravity II: First Order Realizations of Second Order Lagrangians
• Modified Hamiltonian formalism for Regge Teitelboim Cosmology