Related papers: Correspondence Between Classical and Quantum Theor…
An analogue of the Moyal star product is presented for the deformed oscillator algebra. It contains several homotopy-like additional integration parameters in the multiplication kernel generalizing the differential Moyal star-product…
We present a first attempt to apply the approach of deformation quantization to linearized Einstein's equations. We use the analogy with Maxwell equations to derive the field equations of linearized gravity from a modified Maxwell…
We use a deformed differential structure to obtain a curved metric by a deformation quantization of the flat space-time. In particular, by setting the deformation parameters to be equal to physical constants we obtain the…
Guided by recent developments towards the implementation of the deformation quantization program within the Loop Quantum Cosmology (LQC) formalism, in this paper we address the introduction of both the integral and differential…
In this study, we present a modified quantum theory, denoted as $QT^\ast$, which introduces mass-dependent decoherence effects. These effects are derived by averaging the influence of a proposed global quantum fluctuation in position and…
We provide and discuss complex analytic methods for overcoming the formal character of formal deformation quantization. This is a necessity for returning to physically meaningful statements, and accounts for the fact that the formal…
We develop a complete theory of non-formal deformation quantization exhibiting a nonzero minimal uncertainty in position. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on…
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…
In this paper, the Higgs-like approach is used to analyze the quantum dynamics of a harmonic oscillator constrained on a circle. We obtain the Hamiltonian of this system as a function of the Cartesian coordinate of the tangent line through…
The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a…
Deformation theory refers to an apparatus in many parts of math and physics for going from an infinitesimal (= first order) deformation to a full deformation, either formal or convergent appropriately. If the algebra being deformed is that…
The Bohr-Sommerfeld approximation to the eigenvalues of a one-dimensional quantum Hamiltonian is derived through order $\hbar^2$ (i.e., including the first correction term beyond the usual result) by means of the Moyal star product. The…
In his celebrated paper Kontsevich has proved a theorem which manifestly gives a quantum product (deformation quantization formula) and states that changing coordinates leads to gauge equivalent star products. To illuminate his procedure,…
Given a holomorphic Hermitian vector bundle and a star-product with separation of variables on a pseudo-Kaehler manifold, we construct a star product on the sections of the endomorphism bundle of the dual bundle which also has the…
We define a Fr\'echet topology on the space $C^\infty(X)[[\hbar]]$ of formal smooth functions on a symplectic manifold $X$, by constructing a sequence of semi-norms on it. For any star product $\star$ on $C^\infty(X)[[\hbar]]$ making it a…
For a wide set of quantum systems it is demonstrated that the quantum regime can be considered as the transient phase while the final classical statistical regime is a permanent state. A basis where exact matrix decoherence appears for…
Affine variables, which have the virtue of preserving the positive-definite character of matrix-like objects, have been suggested as replacements for the canonical variables of standard quantization schemes, especially in the context of…
We propose a new formula for the star product in deformation quantization of Poisson structures related in a specific way to a variational problem for a function $S$, interpreted as the action functional. Our approach is motivated by…
The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…
We study quantum moment maps of $G$-invariant star products, which are a quantum analogue of the moment map for classical Hamiltonian systems. Introducing an integral representation, we show that any quantum moment map for a $G$-invariant…