Related papers: On Noncommutative Quantum Mechanics and the Black-…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
New method of quantization is presented. It is based on classical Newton-Lagrange equations of motion (representing the fundamental physical law of mechanics) rather than on their traditional Lagrangian and/or Hamiltonian precursors. It is…
The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it…
A new form of quasiclassical space-time dynamics for constrained systems reveals how quantum effects can be derived systematically from canonical quantization of gravitational systems. These quasiclassical methods lead to additional fields,…
The physical world is quantum. However, our description of the quantum physics still relies much on concepts in classical physics and in some cases with `quantized' interpretations. The most important case example is that of spacetime. We…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
Quantum fluctuations of some systems vanish not only in the limit $\hbar\to 0$, but also as some other parameters (such as $1\over N$, the inverse of the number of `colors' of a Yang-Mills theory) vanish. These lead to new classical limits…
We present the state of the art regarding the relation between the physics of Quantum Black Holes and Noncommutative Geometry. We start with a review of models proposed in the literature for describing deformations of General Relativity in…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
In this paper such Riemann metrics are established whose Laplace-Beltrami operators are identical to familiar Hamilton operators of elementary particle systems. Such metrics are the natural positive definite invariant metrics defined on…
In this paper, starting from vortices we are finally lead to a treatment of Fermions as Kerr-Newman type Black Holes wherein we identify the horizon at the particle's Compton wavelength periphery. A naked singularity is avoided and the…
It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy,…
We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General…
In this article we model a financial derivative price as an observable on the market state function. We apply geometric techniques to integrating the Heisenberg Equation of Motion. We illustrate how the non-commutative nature of the model…
Recently, a quantum mechanical theory of quantum spaces described by a large $N$ non-commutative coordinates is proposed as a model for quantum gravity [1]. In this paper, we construct Kerr black hole as a rotating noncommutative geometry…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…