Related papers: Geometric quantization of generalized oscillator
This paper analyzes the properties of the solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. This analysis reveals the presence of a subspace that may provide an appropriate degree of freedom to…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion for three singular systems are obtained as total differential equations in many variables. The integrability conditions for these syatems lead us to the…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we…
Deformation quantization and geometric quantization on K\"ahler manifolds give the mathematical description of the algebra of quantum observables and the Hilbert spaces respectively, where the later forms a representation of quantum…
Beyond the quantum Markov approximation, we calculate the geometric phase of a two-level system driven by a quantized magnetic field subject to phase dephasing. The phase reduces to the standard geometric phase in the weak coupling limit…
For any orthogonal polynomials system on real line we construct an appropriate oscillator algebra such that the polynomials make up the eigenfunctions system of the oscillator hamiltonian. The general scheme is divided into two types: a…
When quantum mechanical qubits as elements of two dimensional complex Hilbert space are generalized to elements of even subalgebra of geometric algebra over three dimensional Euclidian space, geometrically formal complex plane becomes…
Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum,…
A family of geometric models of quantum relativistic rotating oscillator is defined by using a set of one-parameter deformations of the static (3+1) de Sitter or anti-de Sitter metrics. It is shown that all these models lead to the usual…
The usual full- and half-harmonic oscillators are turned into field theories, and that behavior is examined using canonical and affine quantization. The result leads to a valid affine quantization of the half harmonic oscillator field…
A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.
Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…
The method of geometrical quantization of symplectic manifolds is applied to constructing infinite dimensional irreducible unitary representations of the algebra of functions on the compact quantum group $SU_q(2)$. A formulation of the…
On logarithmic paper some real algebraic curves look like smoothed broken lines. Moreover, the broken lines can be obtained as limits of those curves. The corresponding deformation can be viewed as a quantization, in which the broken line…
The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium…
A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally-spaced spectrum and appropriate ladder operators connecting the eigenstates. The…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…
In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian…