Hamiltonian dynamics of extended objects: Regge-Teitelboim model

Abstract

We consider the Regge-Teitelboim model for a relativistic extended object embedded in a fixed background Minkowski spacetime, in which the dynamics is determined by an action proportional to the integral of the scalar curvature of the worldvolume spanned by the object in its evolution. In appearance, this action resembles the Einstein-Hilbert action for vacuum General Relativity: the equations of motion for both are second order; the difference is that here the dynamical variables are not the metric, but the embedding functions of the worldvolume. We provide a novel Hamiltonian formulation for this model. The Lagrangian, like that of General Relativity, is linear in the acceleration of the extended object. As such, the model is not a genuine higher derivative theory, a fact reflected in the order of the equations of motion. Nevertheless, as we will show, it is possible as well as useful to treat it as a `fake' higher derivative system, enlarging the phase space appropriately. The corresponding Hamiltonian on this phase space is constructed: it is a polynomial. The complete set of constraints on the phase space is identified. The fact that the equations of motion are of second order in derivatives of the field variables manifests itself in the Hamiltonian formulation through the appearance of additional constraints, both primary and secondary. These new constraints are second class. In this formulation, the Lagrange multipliers implementing the primary constraints get identified as accelerations. This is a generic feature of any Lagrangian linear in the acceleration possessing reparametrization invariance.

9 pages

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• Black Hole Entropy from Loop Quantum Gravity
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• The G_Newton --> 0 Limit of Euclidean Quantum Gravity
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Cited by in corpus (13)

• Constraint algebra for Regge-Teitelboim formulation of gravity
• A pure Dirac's canonical analysis for four-dimensional BF theories
• Hamiltonian study for Chern-Simons and Pontryagin theories
• Hamiltonian dynamics and gauge symmetry for three-dimensional Palatini theory with cosmological constant
• Hamiltonian dynamics of an exotic action for gravity in three dimensions
• Faddeev-Jackiw quantization of four dimensional BF theory
• External time canonical formalism for gravity in terms of embedding theory
• Dark Energy from the Fifth Dimension
• Dirac's and Generalized Faddeev-Jackiw brackets for Einstein's theory in G $\to 0$ limit
• Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory
• Hydrogen-like Spectrum of Spontaneously Created Brane Universes with deSitter Ground State
• Modified Hamiltonian formalism for Regge Teitelboim Cosmology
• Faddeev-Jackiw and Canonical Analysis of the Jackiw-Teitelboim model written as a BF theory