Related papers: The Hamilton-Jacobi Equations for Strings and p-Br…
We review here some conventional as well as less conventional aspects of the time-independent and time-dependent Hamilton-Jacobi (HJ) theory and of its connections with Quantum Mechanics. Less conventional aspects involve the HJ theory on…
We provide Sobolev estimates for solutions of first order Hamilton-Jacobi equations with Hamiltonians which are superlinear in the gradient variable. We also show that the solutions are differentiable almost everywhere. The proof relies on…
We study the relationship between static p-brane solitons and cosmological solutions of string theory or M-theory. We discuss two different ways in which extremal p-branes can be generalised to non-extremal ones, and show how wide classes…
The time dependent Eikonal equation is a Hamilton-Jacobi equation with Hamiltonian $H(P)=|P|$, which is not strictly convex nor smooth. The regularizing effect of Hamiltonian for the Eikonal equation is much weaker than that of strictly…
We construct the string field Hamiltonian for $c=1-\frac{6}{m(m+1)}$ string theory in the temporal gauge. In order to do so, we first examine the Schwinger-Dyson equations of the matrix chain models and propose the continuum version of…
Hamilton-Jacobi theory provides a natural starting point for a covariant description of the gravitational field. Using a spatial gradient expansion, one may solve for the phase of the wavefunction by using a line-integral in superspace.…
The Hamiltonian analysis of Polyakov action is reviewed putting emphasis in two topics: Dirac observables and gauge conditions. In the case of the closed string it is computed the change of its action induced by the gauge transformation…
Lagrangian submanifolds are becoming a very essential tool to generalize and geometrically understand results and procedures in the area of mathematical physics. Here we use general Lagrangian submanifolds to provide a geometric version of…
We present a new $(p - 1)$-brane solution to Einstein's equations in a general space-time dimension. This solution is a natural generalization of the stringlike defect solution with codimension 2 in 6 space-time dimensions, which has been…
We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} Hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the generalized…
We show how to write a set of brackets for the Langevin equation, describing the dissipative motion of a classical particle, subject to external random forces. The method does not rely on an action principle, and is based solely on the…
It has been shown that given a classical background in string theory which is independent of $d$ of the space-time coordinates, we can generate other classical backgrounds by $O(d)\otimes O(d)$ transformation on the solution. We study the…
In the present article, we construct a 2D formulation of quantum gravity in the framework of a deterministic theory. In this context, a Quantum stationary Hamilton-Jacobi equation is derived from the Klein- Gordon equation written in the…
The classical confinement condition of test particles to a brane universe in the absence of non-gravitational forces is transformed using the Hamilton-Jacobi formalism. The transformed condition provides a direct criterion for selecting in…
The aim of this paper is to understand the relation between the canonical Hamilton-Jacobi equation for Maxwell's electrodynamics, which is an equation with variational derivatives for a functional of field configurations, and the covariant…
We discuss construction of classical time dependent solutions in open string (field) theory, describing the motion of the tachyon on unstable D-branes. Despite the fact that the string field theory action contains infinite number of time…
We study classical dynamics of an open string tachyon $T$ of unstable D$p$-brane coupled to the gauge field $A_\mu$. In the vacuum with vanishing potential, V=0, two fluid-like degrees of freedom, string fluid and tachyon matter, survive…
We calculate boundary states for general string fields in the KBc subalgebra under some regularity conditions based on the construction by Kiermaier, Okawa, and Zwiebach. The resulting boundary states are always proportional to that for the…
We study the dynamics of an open membrane with a cylindrical topology, in the background of a constant three form. We use the action, due to Bergshoeff, London and Townsend, to study the noncommutativity properties of the boundary string…
We propose the action for the nonrelativistic string invariant under general coordinate transformations on the string worldsheet. The Hamiltonian formulation for the nonrelativistic string is given. Particular solutions of the…