Related papers: Quantum Geometry and Quantum Mechanics of Integrab…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…
We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to…
Integrable quantum field theories can be regularized on the lattice while preserving integrability. The resulting theory on the lattice are integrable lattice models. A prototype of such a regularization is the correspondence between…
This is a review of the results related to generalizations of the notion of $\tau$-function and integrable hierarchies and to their interpretation within the group theory framework that admits an immediate quantization procedure. Different…
Decoherence in quantum systems which are classically chaotic is studied. It is well-known that a classically chaotic system when quantized loses many prominent chaotic traits. We show that interaction of the quantum system with an…
Quantum Hamilton-Jacobi quantization scheme uses the singularity structure of the potential of a quantum mechanical system to generate its eigenspectrum and eigenfunctions, and its efficacy has been demonstrated for several well known…
In quantum electrodynamics a classical part of the S-matrix is normally factored out in order to obtain a quantum remainder that can be treated perturbatively without the occurrence of infrared divergences. However, this separation, as…
Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Here, we introduce a decoherence process due to quantum gravity effects. We assume a foamy…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
The so-called topos approach provides a radical reformulation of quantum theory. Structurally, quantum theory in the topos formulation is very similar to classical physics. There is a state object, analogous to the state space of a…
Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system…
The dynamics of any classical-mechanics system can be formulated in the reparametrization-invariant (RI) form (that is we use the parametric representation for trajectories, ${\bf x}={\bf x}(\tau)$, $t=t(\tau)$ instead of ${\bf x}={\bf…
It is shown that in two-state quantum theory, a generic quantum state can be described by a non-computable real number. In terms of this, the criterion for measurement outcome is simply and deterministically defined. This demonstration is…
Quantum relativity as a generalized, or rather deformed, version of Einstein relativity with a linear realization on a classical six-geometry beyond the familiar setting of space-time offer a new framework to think about the quantum…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
So-called hidden variables introduced in quantum mechanics by de Broglie and Bohm have changed their initial enigmatic meanings and acquired quite reasonable outlines of real and measurable characteristics. The start viewpoint was the…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…