Related papers: Classical q-deformed dynamics
Several Clifford algebras that are covariant under the action of a Lie algebra $g$ can be deformed in a way consistent with the deformation of $Ug$ into a quantum group (or into a triangular Hopf algebra) $U_qg$, i.e. so as to remain…
Based on the q-deformed oscillator algebra, we study the behavior of the mean occupation number and its analogies with intermediate statistics and we obtain an expression in terms of an infinite continued fraction, thus clarifying…
We define a generalized $(q;\alpha,\beta,\gamma;\nu)$-deformed oscillator algebra and study the number of its characteristics. We describe the structure function of deformation, analyze the classification of irreducible representations and…
This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We show the interest of such algebras for fractional supersymmetric quantum mechanics, angular momentum theory and…
This paper investigates the dynamics of quantum analogs of classical impact oscillators to explore how complex nonlinear behaviors manifest in quantum systems. While classical impact oscillators exhibit chaos and bifurcations, quantum…
de-Broglie--Bohm causal interpretation of canonical quantum gravity in terms of Ashtekar new variables is built. The Poisson brackets of (deBroglie--Bohm) constraints are derived and it is shown that the Poisson bracket of Hamiltonian with…
The Lie and module (Rinehart) algebraic structure of vector fields of compact support over C infinity functions on a (connected) manifold M define a unique universal non-commutative Poisson * algebra. For a compact manifold, a…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
We revise the technique of semiclassical effective dynamics, in particular reexamining the evaluation of Poisson structure of the so-called central moments capturing quantum corrections, providing a systematic, pedagogical, and efficient…
The quantization problem for the trace-bracket algebra, derived from double Poisson brackets, is discussed. We obtain a generalization of the boundary YBE (or so-called ABCD-algebra) for the quantization of quadratic trace-brackets. A…
The existing approaches to quantization of gravity aim at giving quantum description of 3-geometry following to the ideas of the Wheeler -- DeWitt geometrodynamics. In this description the role of gauge gravitational degrees of freedom is…
In this paper the q-deformed $W$ algebra $\WW_q$ is constructed, whose nontrivial quantum group structure is presented.
Classical gravitational evolution admits an elegant and compact re-expression in terms of gauge covariant generalizations of Lie derivatives with respect to a spatial phase space dependent $su(2)$ valued vector field called the Electric…
We explain how to translate several recent results in derived algebraic geometry to derived differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie groupoids, smooth stacks and derived generalisations, and…
In this work, we develop a q-deformed scalar-tensor theory of gravitation by combining Verlinde's entropic gravity paradigm with statistical deformation effects. The resulting model modifies the Brans-Dicke framework through a deformation…
We formulate Yang-Mills theory in terms of the large-N limit, viewed as a classical limit, of gauge-invariant dynamical variables, which are closely related to Wilson loops, via deformation quantization. We obtain a Poisson algebra of these…
The interaction of a quantum deformed oscillator with the environment is studied deriving a master equation whose form strongly depends on the type of deformation.
Quantum Mechanics is revisited as the appropriate theoretical framework for the description of the outcome of experiments that rely on the use of classical devices. In particular, it is emphasized that the limitations on the measurability…
Poisson algebraic structures on current manifolds (of maps from a finite dimensional Riemannian manifold into a 2-dimensional manifold) are investigated in terms of symplectic geometry. It is shown that there is a one to one correspondence…
Viewed as approximations to quantum mechanics, classical evolutions can violate the positive-semidefiniteness of the density matrix. The nature of this violation suggests a classification of dynamical systems based on classical-quantum…