Related papers: Canonical Nambu mechanics: relevance to string/M-t…
This is a summary of a talk at Strings2000 explaining three ways in which string theory and M-theory are related to the mathematics of K-theory.
We study Hamiltonian analysis of three-dimensional advection flow $\mathbf{\dot{x}}=\mathbf{v}({\bf x})$ of incompressible nature $\nabla \cdot {\bf v} ={\bf 0}$ assuming that dynamics is generated by the curl of a vector potential…
Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise,…
We consider solutions to the $\mu$-problem originating in the effective low energy theories, of N=1 orbifold compactifications of the heterotic string, after supersymmetry breaking. They are consistent with the invariance of the one loop…
Most nonabelian gauge theories admit the existence of conserved and quantized topological charges as generalizations of the Dirac monopole. Their interactions are dictated by topology. In this paper, previous work in deriving classical…
We give an introductory review of Fourier-Mukai transforms and their application to various aspects of moduli problems, string theory and mirror symmetry. We develop the necessary mathematical background for Fourier-Mukai transforms such as…
In this paper, which is a revised version of the author's PhD thesis, we analyze two different applications of string theory. In the first part, we focus on four dimensional compactifications of Type II string theories preserving N=1…
We study the dynamics of strings by means of a distribution function f(A, B, x, t) defined on a 9+1D phase space, where A and B are the correlation vectors of right- and left-moving waves. We derive a transport equation (an analogous to…
We study the self-similar motion of a string in a self-similar spacetime by introducing the concept of a self-similar string, which is defined as the world sheet to which a homothetic vector field is tangent. It is shown that in Nambu-Goto…
Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…
Here we provide the contributions' abstracts published in a volume we edited as a special issue in International Journal of Modern Physics B. The volume deals with the recent progress in quantifying quantum correlations beyond the generic…
The Hamilton-Jacobi formalism of constrained systems is used to study superstring. That obtained the equations of motion for a singular system as total differential equations in many variables. These equations of motion are in exact…
N=2 heterotic strings may provide a window into the physics of M-theory radically different than that found via the other supersymmetric string theories. In addition to their supersymmetric structure, these strings carry a four-dimensional…
A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit…
Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…
Momentum map is a reduction procedure that reduces the dimension of a Hamiltonian system to the lower ones. It is shown that behavior of the action-angle variables under the momentum map generates the new action-angle variables for the…
It is shown that the Dirac-nambu-Goto brane can be described as a point particle in an infinite dimensional brane space with a particular metric. This suggests a generalization to brane spaces with arbitrary metric, including the "flat"…
A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new…
Using as a springboard a three-way debate between theoretical physicist Lee Smolin, philosopher of science Nancy Cartwright and myself, I address in layman's terms the issues of why we need a unified theory of the fundamental interactions…
A survey of topics of recent interest in Hamiltonian and Lagrangian dynamical systems, including accessible discussions of regularization of the central force problem; inequivalent Lagrangians and Hamiltonians; constants of central force…