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In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent and independent. In order to do so, we construct a Hamilton--Jacobi theory for these systems following two approaches, obtaining two different…
A time-dependent completely integrable Hamiltonian system is quantized with respect to time-dependent action-angle variables near an instantly compact regular invariant manifold. Its Hamiltonian depends only on action variables, and has a…
The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme…
This paper provides new theoretical connections between multi-time Hamilton-Jacobi partial differential equations and variational image decomposition models in imaging sciences. We show that the minimal values of these optimization problems…
For constrained system which has several independent first integrals, we give a new stabilization method which named adjustment-stabilization method. It can stabilize all known constants of motion for a given dynamical system very well…
A formalism is developed to obtain the energy eigenvalues of spatially confined quantum mechanical systems in the framework of The usual WKB and MAF methods. The technique is applied to three different cases,viz one dimensional Harmonic…
The Hamilton-Jacobi analysis of three dimensional gravity defined in terms of Ashtekar-like variables is performed. We report a detailed analysis where the complete set of Hamilton-Jacobi constraints, the characteristic equations and the…
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…
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…
We investigate canonical quantization of a general spherically symmetric spacetimes with a massless scalar-field source and examine the associated constraint algebra. The spacetimes are quantized using Dirac's quantization method for…
This paper is devoted to discrete mechanical systems subject to external forces. We introduce a discrete version of systems with Rayleigh-type forces, obtain the equations of motion and characterize the equivalence for these systems.…
We will analyze the constraint structure of the Einstein-Hilbert first-order action in two dimensions using the Hamilton-Jacobi approach. We will be able to find a set of involutive, as well as a set of non-involutive constraints. Using…
We extend the quantization \`a la Faddeev-Jackiw for non-autonomous singular systems. This leads to a generalization of the Schr\"odinger equation for those systems. The method is exemplified by the quantization of the damped harmonic…
We derive the Hamilton equations of motion for a constrained system in the form given by Dirac, by a limiting procedure, starting from the Lagrangean for an unconstrained system. We thereby ellucidate the role played by the primary…
The semiclassical solution of quantum Dirac constraints in generic constrained system is obtained by directly calculating in the one-loop approximation the gauge field path integral with relativistic gauge fixing procedure. The gauge…
Based on a method developed earlier for a finite-dimensional mechanical system, the problem of path integral reduction for scalar electrodynamics is considered. Using the Coulomb gauge, the stochastic differential equations for the reduced…
A hybrid system is a system whose dynamics is given by a mixture of both continuous and discrete transitions. In particular, these systems can be utilised to describe the dynamics of a mechanical system with impacts. Based on the approach…
The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
We use the ideas of symplectic quantization for quantizing fields in finite volumes. We consider, as examples, the Klein-Gordon and electromagnetic fields in three dif- ferent boxes. As a second idea we consider the given boundary…