Related papers: Comment on `Do we have a consistent non-adiabatic …
A convenient formalism is developed to treat classical dynamical systems involving $(p=2)$ parafermionic and parabosonic dynamical variables. This is achieved via the introduction of a parabracket which summarizes the paracommutation…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
Classical and quantum world views differ in peculiar ways. Understanding decisive quantum features -- for which no classical explanation exist -- and their interrelations is of foundational interest. Moreover, recognizing non-classical…
This is an up-to-date survey of the p-mechanical construction (see funct-an/9405002, quant-ph/9610016, math-ph/0007030, quant-ph/0212101, quant-ph/0303142), which is a consistent physical theory suitable for a simultaneous description of…
A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…
75 years after the term "entanglement" was coined to a peculiar feature inherent to quantum systems, the connection between quantum and classical mechanics remains an open problem. Drawing on recent results obtained in semiclassical…
While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…
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…
We present recent developments in the theory of Nambu mechanics, which include new examples of Nambu-Poisson manifolds with linear Nambu brackets and new representations of Nambu-Heisenberg commutation relations.
In a recent series of papers we have analyzed a certain deformation of the canonical commutation relations producing an interesting functional structure which has been proved to have some connections with physics, and in particular with…
These notes describe some links between the group $\mathrm{SL}_2(\mathbb{R})$, the Heisenberg group and hypercomplex numbers---complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this…
The reinterpretation of quantum mechanical formalism in terms of a classical model with a continuous material "$\Psi$-field" acting upon a point-like particle which is subjected to large friction and random forces is proposed. This model…
This paper extends the classical theory of joinings of measurable dynamical systems to the noncommutative setting from several interconnected points of view. Among these is a particularly fruitful identification of joinings with equivariant…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, 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,…
Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by 'superposition' in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
In this paper we introduce a kind of "noncommutative neighbourhood" of a semiclassical parameter corresponding to the Planck constant. This construction is defined as a certain filtered and graded algebra with an infinite number of…
$P$-divisibility is a central concept in both classical and quantum non-Markovian processes; in particular, it is strictly related to the notion of information backflow. When restricted to a fixed commutative algebra generated by a complete…