相关论文: Quantum Mechanical Observables under a Symplectic …

We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…

We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…

Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in…

We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…

In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…

The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kaehler manifold. The classical principles of Quantum Mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability…

The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincar\'e symmetry of field theory can be extended to the larger conformal symmetry. We use…

Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…

An observable on a quantum structure is any $\sigma$-homomorphism of quantum structures from the Borel $\sigma$-algebra into the quantum structure. We show that our partial information on an observable known only for all intervals of the…

In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…

We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…

We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual…

We quantise complex, infinite-dimensional projective space CP(H). We apply the result to quantise a complex, finite-dimensional, classical phase space C whose symplectic volume is infinite, by holomorphically embedding it into CP(H). The…

A review is given of recent work aimed at constructing a quantum theory of cosmology in which all observables refer to information measurable by observers inside the universe. At the classical level the algebra of observables should be…

We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of $n$-dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of…

In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…

In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including…

The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…

In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame.…

We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space…