Related papers: Faddeev-Jackiw Quantization of Non-Autonomous Sing…
We quantize the (2+1)-dimensional self-dual and Maxwell-Chern-Simons theories by using the Faddeev-Jackiw formulation and compare the results with those of the Dirac formalism.
I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Dirac's formalism I construct for each case the…
We numerically compute eigenvalues of the non-self-adjoint Zakharov--Shabat problem in the semiclassical regime. In particular, we compute the eigenvalues for a Gaussian potential and compare the results to the corresponding (formal) WKB…
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…
In this paper we study the quantization of the nonlinear oscillator introduced by Mathews and Lakshmanan. This system with position-dependent mass allows a natural quantization procedure and is shown to display shape invariance. Its energy…
It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and $R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above…
The gauge equivalent formulation of the Faddeev-Skyrme model is used for the study of the quantum theory. The rotational quantum excitations around the soliton solution of Hopf number unity are investigated by the method of collective…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
The treatment of confining interactions in non-relativistic three-quark systems is revised. Usually in the Faddeev equations the Faddeev components are coupled by the total potential. In the new treatment the Faddeev components are coupled…
We study Lagrangian systems with a finite number of degrees of freedom that are non-local in time. We obtain an extension of Noether theorem and Noether identities to this kind of Lagrangians. A Hamiltonian formalism is then set up for this…
We study the random attractors associated with the stochastic fractional Schr\"odinger equation on $\mathbb{R}^n$. Utilizing the stochastic Strichartz estimates for the damped fractional Schr\"odinger equation with Gaussian noise, we show…
The quantization of the SU(2)$\times $U(1) gauge-symmetric electroweak theory is performed in the Hamiltonian path-integral formalism. In this quantization, we start from the Lagrangian given in the unitary gauge in which the unphysical…
In this paper, the theory of the fractional singular Lagrangian systems is investigated with second order derivatives. The fractional quantization for these systems is examined using the WKB approximation. The Hamilton Jacobi treatment can…
Recently, it is shown that the extended phase space formulation of quantum mechanics is a suitable technique for studying the quantum dissipative system. Here, as an application of this formalism, we consider a dissipative system of charged…
For a singular oscillator, the Schrodinger equation is obtained an equation of eigenvalues, and the dependence of energy on the self-adjoint extension parameter is established. It is shown that the self-adjoint extension violates the…
We shortly recall the derivation of the Faddeev-Yakubovsky differential equations and point out their main advantages. Then we give a review of the numerical approaches used to solve the bound-state and scattering problems for the three-…
One presents a phase-space noncommutative extension of Quantum Cosmology in the context of a Kantowski-Sachs (KS) minisuperspace model. We obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and…
We obtain scattering for the 3D Zakharov system with non-radial small data in the energy space with angular regularity of degree one. The main ingredient is a generalized Strichartz estimate for the Schr\"odinger equation in the space of…
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…
We study collective phenomena of self-propagating particles using the nonlinear Kramers equation. A solitary wave state appears from an instability of the spatially uniform ordered state with nonzero average velocity. Two solitary waves…