Related papers: Symplectic Structure in Brane Mechanics
This article is based on the covariant canonical formalism and corresponding symplectic structure on phase space developed by Witten, Zuckerman and others in the context of field theory. After recalling the basic principles of this…
Using a fully covariant formalism given by Carter for the deformation dynamics of p-branes governed by the Dirac-Nambu-Goto action in a curved background, it is proved that the corresponding Witten's phase space is endowed with a covariant…
Using a strongly covariant formalism given by Carter for the deformations dynamics of p-branes in a curved background and a covariant and gauge invariant geometric structure constructed on the corresponding Witten's phase space, we identify…
Using a covariant and gauge invariant geometric structure constructed on the Witten covariant phase space for Dirac-Nambu-Goto bosonic p-branes propagating in a curved background, we find the canonically conjugate variables, and the…
This paper presents a "historical" formalism for dynamical systems, in its Hamiltonian version (Lagrangian version was presented in a previous paper). It is universal, in the sense that it applies equally well to time dynamics and to field…
We show that the Witten covariant phase space for p-branes with thickness in an arbitrary background is endowed of a symplectic potential, which although is not important to the dynamics of the system, plays a relevant role on the phase…
Dirac's method for variations of a brane embedded in co-dimension one is demonstrated. The variation in the location of the brane invokes a rest frame formulation of the 'sandwiched' brane action. We first demonstrate the necessity of this…
We extend a recent analysis of gravitational perturbations on Dirac-Nambu-Goto strings, membranes and higher dimensional branes. In an arbitrary gauge, it is shown that the relevant first order equations governing the displacement vector of…
We show that there exist a nontrivial contribution on the Witten covariant phase space when the Gauss-Bonnet topological term is added to the Dirac-Nambu Goto action describing strings, because of the geometry of deformations is modified,…
Starting from generic bilinear Hamiltonians, constructed by covariant vector, bivector or tensor fields, it is possible to derive a general symplectic structure which leads to holonomic and anholonomic formulations of Hamilton equations of…
We show that the symplectic current obtained from the boundary term, which arises in the first variation of a local diffeomorphism invariant action, is covariantly conserved for any gravity theory described by that action. Therefore, a…
It is well known that the Lagrangian and the Hamiltonian formalisms can be combined and lead to "covariant symplectic" methods. For that purpose a "pre-symplectic form" has been constructed from the Lagrangian using the so-called Noether…
A covariant simultaneous action for branes in an arbitrary curved background spacetime is considered. The action depends on a pair of independent field variables, the brane embedding functions, through the canonical momentum of a…
We discuss some aspects of the relation between space-time properties of branes in string theory, and the gauge theory on their worldvolume, for models invariant under four supercharges in three and four dimensions. We show that a simple…
We use a new formula for the symplectic structure on the phase space of open string field theory to evaluate the energy of a D-brane carrying a constant electric flux. This is shown to be consistent with the energy computed using the…
We show how to translate boundary conditions into constraints in the symplectic quantization method by an appropriate choice of generalized variables. This way the symplectic quantization of an open string attached to a brane in the…
The great deal in noncommutative (NC) field theories started when it was noted that NC spaces naturally arise in string theory with a constant background magnetic field in the presence of $D$-branes. Besides their origin in string theories…
We show how to cast an interacting system of M--branes into manifestly gauge-invariant form using an arrangement of higher-dimensional Dirac surfaces. Classical M--theory has a cohomologically nontrivial and noncommutative set of gauge…
The structure of a diffeomorphism invariant Lagrangians for an extended object W embedded in a bulk space M is discussed by following a close analogy with the relativistic particle in electromagnetic field as a system that is…
The covariant canonical formalism is a covariant extension of the traditional canonical formalism of fields. In contrast to the traditional canonical theory, it has a remarkable feature that canonical equations of gauge theories or gravity…