Hamilton-Jacobi Formulation of Constrained Particles and Strings

Abstract

In this dissertation, we explore various aspects of the singular physical systems, which are treated by using the Hamiltonian formulation of constrained systems. The Hamilton-Jacobi formalism, are presented for supersymmetry models of supersymmetric particles and string. The formalism is applied to study the dynamics of massive Brink-Schwarz superparticle and massless Seigel superparticle with simple supersymmetry N = 1, possesses in the most popular superspace in physics R4│4. The integrability conditions are satisfied, so the systems are integrable. We have applied the method to obtain the classical dynamics in phase-space of massless spinning superparticles. By proceeding in the same way, we analyze the dynamics of superparticle with extended supersymmetric N = 2 coupled with an external superpotential, and various applications of superstring. Firstly, we generalize this approach for a string that is propagating in 4D superspace. Secondly, the example of Green-Schwarz superstring, which provides the most realistic string models has been formulated. Besides, a mechanical model of D = 11 superstring is constructed, and in terms of the Hamilton-Jacobi formalism the equations of motion are derived and discussed, as total differential equations in many variables.