Hamiltonian analysis for linearly acceleration-dependent Lagrangians

Abstract

We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defned quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identifed. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian formulation of covariant feld theories.

33 pages, no figures

References in corpus (10)

• Ostrogradski approach for the Regge-Teitelboim type cosmology
• On the instability of classical dynamics in theories with higher derivatives
• New Hamiltonian analysis of Regge Teitelboim minisuperspace cosmology
• The Geometry Of Higher-Order Hamilton Spaces; Applications to Hamiltonian Mechanics
• Quantum modified Regge-Teitelboim cosmology
• Quantum charged rigid membrane
• Gauge symmetry and Virasoro algebra in quantum charged rigid membrane -- a first order formalism
• Two-dimensional metric and tetrad gravities as constrained second order systems
• A path integral leading to higher-order Lagrangians
• A note on the Hamiltonian formalism for higher-derivative theories

Cited by in corpus (10)

• Interacting Diffusive Unified Dark Energy and Dark Matter from Scalar Fields
• A Hamilton-Jacobi formalism for higher order implicit systems
• Hamilton-Jacobi approach for Regge-Teitelboim cosmology
• Deformation quantization of the Pais-Uhlenbeck fourth order oscillator
• Reductions of Topologically Massive Gravity I: Hamiltonian Analysis of The Second Order Degenerate Lagrangians
• Ostrogradsky-Hamilton approach to geodetic brane gravity
• Reductions of Topologically Massive Gravity II: First Order Realizations of Second Order Lagrangians
• Holographic relationships in Lovelock type brane gravity
• Variational symmetries of Lagrangian systems with higher-order derivatives
• Hamilton-Jacobi approach for linearly acceleration-dependent Lagrangians