Related papers: The semantics of the canonical commutation relatio…
Non-Fock representations of the canonical commutation relations modeled over an infinite-dimensional nuclear space are constructed in an explicit form. The example of the nuclear space of smooth real functions of rapid decrease results in…
We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
The model of generalized quons is described in a purely algebraic way. Commutation relations and corresponding consistency conditions for our generalized quons system are studied in terms of quantum Weyl algebras. Fock space representation…
In statistical mechanics, it is well known that finite-state classical lattice models can be recast as quantum models, with distinct classical configurations identified with orthogonal basis states. This mapping makes classical statistical…
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 discuss quantum non-locality and contextuality, emphasising logical and structural aspects. We also show how the same mathematical structures arise in various areas of classical computation.
The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or…
This paper presents the general theory of canonical transformations of coordinates in quantum mechanics. First, the theory is developed in the formalism of phase space quantum mechanics. It is shown that by transforming a star-product, when…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
In it's usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended…
The canonical formalism for expanding metrics scenarios is presented. Non-unitary time evolution implied by expanding geometry is described as a trajectory over unitarily inequivalent representations at different times of the canonical…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
We give a simple demonstration that the Schr\"odinger equation may be recast as a self-contained second-order Newtonian law for a congruence of spacetime trajectories. This provides a pictorial representation of the quantum state as the…
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…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…