On the time evolution in totally constrained systems with weakly vanishing Hamiltonian

The Dirac method treatment for finite dimensional singular systems with weakly vanishing Hamiltonian leads to obtain the equations of motion in terms of parameter $\tau$. To obtain the correct equations of motion one should use gauge fixing of the form $\tau - f(t)=0$. It is shown that the canonical method leads to describe the evolution in both standard and constrained finite dimensional systems with weakly vanishing Hamiltonian in terms of the physical time $t$, without using any gauge fixing conditions. Besides the operator quantization of the these systems is investigated using the canonical method and it is shown that the evolution of the state $\Psi$ with the time $t$ is described by the Schr/"odinger equation i\frac{\partial \Psi}{\Partial t} = {\hat H}\Psi. The extension of this treatment to infinite dimensional systems is given.Comment: 15 pages, latex, no fiqure

Canonical quantization of systems with time-dependent constraints

The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for the relativistic particle in a plane wave lead us to obtain the canonical phase-space coordinates with out using any gauge fixing condition. As a result of the quantization, we obtain the Klein-Gordon theory for a particle in a plane wave. The path integral quantization for this system is obtained using the canonical path integral formulation method.Comment: 10 pages, latex, no fiqure

Path integral quantization of Yang-Mills theory

Path integral formulation based on the canonical method is discussed. Path integral for Yang-Mills theory is obtained by this procedure. It is shown that gauge fixing which is essential procedure to quantize singular systems by Faddeev's and Popov's method is not necessary if the canonical path integral formulation is used.Comment: 9 pages, latex, no fiqure

Completely and Partially Integrable Systems of Total Differential Equations

Constrained Hamiltonian systems are investigated by using the Hamilton-Jacobi method. Integration of a set of equations of motion and the action function is discussed. It is shown that we have two types of integrable systems: a) ${\it Partially integrable systems}$, where the set of equations of motion is only integrable. b) {\it Completely integrable systems}, where the set of equations of motion and the action function is integrable. Two examples are studied.Comment: Late

The equivalence between the Hamiltonian and the Lagrangian formulations for the parametrization invariant theories

The link between the tratment of singular Lagrangians as field systems and the canonical Hamiltonian approach is studied. It is shown that the singular Lagrangians as field systems are always in exact agreement with the canonical approach for the parametrization invariant theories.Comment: 8 pages, latex, nofiqure

Canonical formulation treatment of a free relativistic spinning particle

The canonical method of constrained system is discussed. The equations of motion for a free relativistic spinning particle are obtained without using gauge fixing conditions. The quantization of this model is discussed.Comment: 7 pages, latex, no fiqure

Path integral formulation of constrained systems with singular-higher order Lagrangian

Systems with singular higher order- Lagrangians are investigated by using the extended form of the canonical method. Besides, the canonical path integral formulation is generalized using the Hamilton- jacobi formulation to investigate singular system

Canonical path integral quantization of Einstein's gravitational field

The connection between the canonical and the path integral formulations of Einstein's gravitational field is discussed using the Hamilton - Jacobi method. Unlike conventional methods, it is shown that our path integral method leads to obtain the measure of integration with no $\delta$- functions, no need to fix any gauge and so no ambiguous deteminants will appear.Comment: 7 pages, Latex, no fiqure

Quantization of singular systems with second order Lagrangians

The path integral formulation of singular systems with second order Lagrangian is studied by using the canonical path integral method. The path integral of Podolsky electrodynamics is studied.Comment: 12 pages, latex, nofiqure

The Hamilton-Jacobi treatment for an abelian Chern-Simons system

The abelian Chern-Simons system is treated as a constrained system using the Hamilton-Jacobi approach. The equations of motion are obtained as total differential equations in many variables. It is shown that their simultaneous solutions with the constraints lead to obtain canonical phase space coordinates and the reduced phase space Hamiltonian with out introducing Lagrange multipliers and with out any additional gauge fixing condition.Comment: 8 pages, latex, no fiqure