Related papers: Quantization over boson operator spaces
We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…
We consider a class of models of self-interacting bosons hopping on a lattice. We show that properly tailored space-temporal coherent control of the single-body coupling parameters allows for universal quantum computation in a given sector…
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…
We review the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analyse the information contained in the solutions of the Wheeler-DeWitt equation and…
As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define…
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 Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…
The Hamiltonian treatment of constrained systems in $G\ddot{u}ler's$ formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a…
We propose a new method of quantization of a wide class of dynamical systems that originates directly from the equations of motion. The method is based on the correspondence between the classical and the quantum Poisson brackets, postulated…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
In quantum physics, the operators associated with the position and the momentum of a particle are unbounded operators and $C^*$-algebraic quantisation does therefore not deal with such operators. In the present article, I propose a…
We have studied the quantum Liouville theory on the Riemann sphere with n>3 punctures. While considering the theory on the Riemann surfaces with n=4 punctures, the quantum theory near an arbitrary but fixed puncture can be obtained via…
We describe a deformation quantization of a modification of Poisson geometry by a closed 3-form. Under suitable conditions it gives rise to a stack of algebras. The basic object used for this aim is a kind of families of Poisson structures…
We construct and characterize quantum Garnier systems in two variables including degenerate cases by certain holomorphic properties under the quantum canonical transformations.
Let $G$ be the complex general linear group and $g$ its Lie algebra equipped with a factorizable Lie bialgebra structure; let $U_h$ be the corresponding quantum group. We construct explicit $U_h$-equivariant quantization of Poisson orbit…
A system of linearly coupled quantum harmonic oscillators can be diagonalized when the system is dynamically stable using a Bogoliubov canonical transformation. However, this is just a particular case of more general canonical…
For linear bose field theories, I show that if a classical Hamiltonian function is strictly positive, then there is a canonical transformation making the evolution orthogonal. This structure theorem is used to analyze the corresponding…
We develop the idea of employing localization systems of Boolean coverings, associated with measurement situations, in order to comprehend structures of Quantum Observables. In this manner, Boolean domain observables constitute structure…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
Quantum Groups can be constructed by applying the quantization by deformation procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to develop an understanding of these structures by investigating dynamical systems…