Hamiltonian dynamics of extended objects

TL;DR

This paper develops a Hamiltonian framework for relativistic extended objects with extrinsic curvature dependence, inspired by ADM formalism, clarifying their phase space structure and constraints.

Contribution

It introduces a Hamiltonian formulation for higher derivative relativistic objects based on extrinsic curvature, including explicit Hamiltonian and constraint analysis.

Findings

Explicit Hamiltonian constructed for the model

Primary and secondary constraints identified

Relationship between conjugate momentum and conserved momentum established

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.