Canonical structure of higher derivative theories

Abstract

The canonical structure of theories whose Lagrangian contains higher powers of time derivatives is often obscured by the nonlinear relationship between the velocities and momenta. We use the Dirac formalism and define a generalized Legendre transform to overcome some of the difficulties associated with inverting the relation between velocities and momenta. We are then able to define a standard single valued symplectic structure on phase space and a compatible single valued Hamiltonian. We demonstrate the application of our formalism in several examples.

19 pages, 2 figures, v2 typos corrected, some references and clarifications added, replaced to agree with published version

References in corpus (4)

• Generalized phase transitions in Lovelock gravity
• Single-Valued Hamiltonian via Legendre-Fenchel Transformation and Time Translation Symmetry
• Hamiltonian description of singular Lagrangian systems with spontaneously broken time translation symmetry
• Branched Hamiltonians and Supersymmetry

Cited by in corpus (11)

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• The two canonical conjugate pairs at the horizon of a D1D5 black hole
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• Canonical formulation of Pais-Ulhenbeck action and resolving the issue of branched Hamiltonian
• Branched Hamiltonians for a class of Velocity Dependent Potentials
• Perusing Buchbinder--Lyakhovich canonical formalism for Higher-Order Theories of Gravity
• Symplectic quantization of multi-field Generalized Proca electrodynamics
• Conflict between some higher-order curvature invariant terms