Related papers: A complete characterization of phase space measure…
Quantization with coherent states allows to " quantize " any space X of parameters. In the case where X is a phase space, this leads to the usual quantum mechanics. But the procedure is much more general, and does not require a symplectic,…
A proposal of how to complete non-relativistic quantum mechanics to a physically meaningful, mathematically precise and logically coherent theory is reviewed. Our proposal leads to a general, non-linear stochastic law for the time-evolution…
We study the behavior of non-relativistic quantum particles interacting with different potentials in the space-times generated by a cosmic string and a global monopole. We find the energy spectra in the presence of these topological defects…
Extended phase space of an elementary (relativistic) system is introduced in the spirit of the Souriau's definition of the `space of motions' for such system. Our formulation is generally applicable to any homogeneous space-time (e.g. de…
We make a critical comparison of relativistic and non-relativistic classical and quantum mechanics of particles in inertial frames and of the open problems in particle localization at the two levels. The solution of the problems of the…
Non-canonical equations of motion are derived from a variational principle written in symplectic form. The invariant measure of phase space and the covariant expression for the entropy are derived from non-canonical transformations of…
The interaction of a moving charged particle with its coherent electromagnetic field is analysed in the framework of non-relativistic quantum mechanics. It is shown that, when this interaction is taken into account, a spatially localized…
This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2)…
For metrizable spaces we replace the notion of almost periodic homeomorphism with a similar notion and verify that the usual characterizations of almost periodic homeomorphisms of compact metric spaces are valid for all metrizable spaces.
Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…
It is shown that the general relativity has a one-parameter compact symmetry and this symmetry is analogous to the phase symmetry of quantum mechanics
We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
A series of successive quantizations is considered, starting with the quantization of a non relativistic or relativistic point particle: 1) quantization of a particle's position, 2) quantization of wave function, 3) quantization of wave…
We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve…
We review some quantum-phase descriptions of optical fields. We focus on real fields that can be generated in practice in various nonlinear optical processes. Thus, we rather avoid discussions of phase formalisms as such and try to exploit…
We describe all the localization observables of a quantum particle in a one-dimensional box in terms of sequences of unit vectors in a Hilbert space. An alternative representation in terms of positive semidefinite complex matrices is…
The continuous transition from a low resolution quantum nondemolition measurement of light field intensity to a precise measurement of photon number is described using a generalized measurement postulate. In the intermediate regime,…
We present a complete study of measure-theoretic area formulas in metric spaces, providing different measurability conditions.
The paper investigates relations between the phase space structure of a quantum field theory ("nuclearity") and the concept of pointlike localized fields. Given a net of local observable algebras, a phase space condition is introduced that…