Related papers: Weyl-Wigner-Moyal formulation of a Dirac quantized…
Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
We show that the covariant analytic mechanics (CAM) is closely related to the De Donder-Weyl (DW) theory. To treat space and time on an equal footing, the DW theory introduces $D$ conjugate fields ($D$ is the dimension of space-time) for…
From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…
One can argue that on flat space $\mathbb{R}^d$ the Weyl quantization is the most natural choice and that it has the best properties (e.g. symplectic covariance, real symbols correspond to Hermitian operators). On a generic manifold, there…
The relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of Hamiltonian systems having no gauge conditions. It is traced out that the two quantization methods may give…
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…
A full consideration of classical and quantum systems with radiation (electromagnetic/gravitational) requires the involvement of a mathematical description in the generalized phase space of high kinematical values. Based on the dispersion…
For an arbitrary simple Lie algebra $\g$ and an arbitrary root of unity $q,$ the closed subsets of the Weyl alcove of the quantum group $U_q(\g)$ are classified. Here a closed subset is a set such that if any two weights in the Weyl alcove…
The Floreanini-Jackiw formulation of the chiral quantum-mechanical system oscillator is a model of constrained theory with only second-class constraints. in the Dirac's classification.The covariant quantization needs infinite number of…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more…
Given a suitable ordering of the positive root system associated with a semisimple Lie algebra, there exists a natural correspondence between Verma modules and related polynomial algebras. With this, the Lie algebra action on a Verma module…
A generalized Weyl quantization formalism for a particle on the circle investigated in \cite{1} is developed. A Wigner function for the state $\hat{\varrho}$ and the kernel $\mathcal{K}$ for a particle on the circle is defined and its…
The Moyal product is used to cast the equation for the metric of a non-hermitian Hamiltonian in the form of a differential equation. For Hamiltonians of the form $p^2+V(ix)$ with $V$ polynomial this is an exact equation. Solving this…
The metaplectic covariance for all forms of the Weyl-Wigner-Groenewold-Moyal quantization is established with different realizations of the inhomogeneous symplectic algebra. Beyond that, in its most general form $W_{\infty}$ -covariance of…
It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first)- class…
We discuss the $q$ deformation of Weyl-Heisenberg algebra in connection with the von Neumann theorem in Quantum Mechanics. We show that the $q$-deformation parameter labels the Weyl systems in Quantum Mechanics and the unitarily…
The system of two relativistic particles with einbein fields is quantized as a constrained system.A method of the introduction of the Newton--Wigner collective coordinate is discussed in presence of different gauge fixing conditions. Some…