Related papers: Quantum Mechanics on the cylinder
The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical…
A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…
In this paper, the principles of the general relativity are used to formulate quantum wave equations for spin-0 and spin-1/2 particles. More specifically, the equations are worked in a Schwarzschild-like metric. As a test, the hydrogen atom…
In this article we present formulae for q-integration on quantum spaces which could be of particular importance in physics, i.e. q-deformed Minkowski space and q-deformed Euclidean space in 3 or 4 dimensions. Furthermore, our formulae can…
We review deformed quantum phase spaces and their realizations in terms of undeformed phase space. In particular, methods of calculation for the star product, coproduct of momenta and twist from realizations are presented, as well as their…
Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…
A non--commutative analogue of the classical differential forms is constructed on the phase--space of an arbitrary quantum system. The non--commutative forms are universal and are related to the quantum mechanical dynamics in the same way…
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…
Three different methods viz. i) a perturbative analysis of the Schr\"odinger equation ii) abstract differential geometric method and iii) a semiclassical reduction of the Wheeler-Dewitt equation, relating Pancharatnam phase to vacuum…
On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum…
The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave…
We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it…
An outline is given how to formulate a relativistic unitarized constituent quark model of mesons in momentum space, employing harmonic quark confinement. As a first step, the momentum-space harmonic-oscillator potential is solved in a…
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schroedinger equations (SE). Despite the success of this representation of the quantum…
In this work we will answer the following question: What remains of Quantum Mechanics when we transform the background space-time into a space modularized by observation or measurement regions ? This new moduli space is constructed by…
The quantum mechanics of one degree of freedom exhibiting the exact conformal SL(2,R) symmetry is presented. The starting point is the classification of the unitary irreducible representations of the SL(2,R) group (or, to some extent, its…
It has been established that endowing classical phase space with a Riemannian metric is sufficient for describing quantum mechanics. In this letter we argue that, while sufficient, the above condition is certainly not necessary in passing…
The gauge variance of wave functionals for a gauge theory quantized in the momentum (curvature) representation is described. It is shown that a gauge transformation gives rise to a cocycle, which for theories in two space-time dimensions is…
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…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…