Related papers: Generalised Virial theorems in Classical and Quant…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
Elaboration of some fundamental relations in three dimensional quantum mechanics is considered taking into account the restricted character of areas in radial distance. In such cases the boundary behavior of the radial wave function and…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
We suggest a somewhat non-standard view on a set of curious, paradoxical from the standpoint of simple classical physics and everyday experience phenomena. There are the quantisation (discrete set of values) of the observables (e.g.,…
A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become…
We present a complete theory, which is a generalization of Bargmann's theory of factors for ray representations. We apply the theory to the generally covariant formulation of the Quantum Mechanics.
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schroedinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the…
In this paper, we will introduce Quantum Toric Varieties which are (non-commutative) generalizations of ordinary toric varieties where all the tori of the classical theory are replaced by quantum tori. Quantum toric geometry is the…
A modified quantum kinetic equation which takes account of the noninertial features of rotating frame is proposed. The vector and axial-vector field components of the Wigner function for chiral fluids are worked out in a semiclassical…
In this dissertation the question of the unification of quantum theory and general relativity is treated. Based on the conceptual structure of these theories and under incorporation of certain ideas from classical philosophy there are…
The standard uncertainty relations (UR) in quantum mechanics are typically used for unbounded operators (like the canonical pair). This implies the need for the control of the domain problems. On the other hand, the use of (possibly…
This note derives the stochastic differential equations and partial differential equation of general hybrid quantum--classical dynamics from the theory of continuous measurement and general (non-Markovian) feedback. The advantage of this…
Products and tensor products are linked by a universal property. Imposing the invariance of the laws of Nature under tensor composition along with Leibniz identity determines quantum and classical mechanics algebraic structure through the…
The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation,…
Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one--dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of…
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…
We derive the generalized chiral kinetic equations which are applicable to the fermions with arbitrary mass. We show how the dynamical magnetic-moment distribution function could lead to spin polarization and electric charge separation. We…
The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role…