Hamiltonian dynamics of extended objects

Abstract

We consider a relativistic extended object described by a reparametrization invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behavior under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations shown to be consistent with the Euler-Lagrange equations.

24 pages, latex

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Cited by in corpus (14)

• Ostrogradski approach for the Regge-Teitelboim type cosmology
• Quantum modified Regge-Teitelboim cosmology
• Hamilton's equations for a fluid membrane
• Quantum charged rigid membrane
• Hamiltonian analysis for linearly acceleration-dependent Lagrangians
• Modified geodetic brane cosmology
• Shell-mediated tunnelling between (anti-)de Sitter vacua
• Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory
• Ostrogradsky-Hamilton approach to geodetic brane gravity
• Hamiltonian dynamics of gonihedric string theory
• Geometrical dynamics of Born-Infeld objects
• Holographic relationships in Lovelock type brane gravity
• Covariant canonical formalism for Dirac-Nambu-Goto bosonic p-branes and the Gauss-Bonnet topological term in string theory
• Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA)