Elias Zafiris

Generalized topological covering systems on quantum events' structures

Homologous operational localization processes are effectuated in terms of generalized topological covering systems on structures of physical events. We study localization systems of quantum events structures by means of Gtothendieck topologies on the base category of Boolean events algebras. We show that a quantum events algebra is represented by means of a Grothendieck sheaf-theoretic fibred structure, with respect to the global partial order of quantum events fibres over the base category of local Boolean frames.

Boolean coverings of quantum observable structure: a setting for an abstract differential geometric mechanism

Abstract We develop the idea of employing localization systems of Boolean coverings, associated with measurement situations, in order to comprehend structures of quantum observables. In this manner, Boolean domain observables constitute structure sheaves of coordinatization coefficients in the attempt to probe the quantum world. Interpretational aspects of the proposed scheme are discussed with respect to a functorial formulation of information exchange, as well as, quantum logical considerations. Finally, the sheaf theoretical construction suggests an operationally intuitive method to develop differential geometric concepts in the quantum regime.

Decoherent histories approach to the arrival time problem

What is the probability of a particle entering a given region of space at any time between

Sheaf-theoretic representation of quantum measure algebras

{t}_{1}

A Categorial Semantic Representation of Quantum Event Structures

and

Differential sheaves and connections : a natural approach to physical geometry

{t}_{2}?

The Homological Kähler-De Rham Differential Mechanism part I: Application in General Theory of Relativity

Standard quantum theory assigns probabilities to alternatives at a fixed moment of time and is not immediately suited to questions of this type. We use the decoherent histories approach to quantum theory to compute the probability of a nonrelativistic particle crossing

Probing Quantum Structure with Boolean Localization Systems

x=0

The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors

during an interval of time. For a system consisting of a single nonrelativistic particle, histories coarse grained according to whether or not they pass through spacetime regions are generally not decoherent, except for very special initial states, and thus probabilities cannot be assigned. Decoherence may, however, be achieved by coupling the particle to an environment consisting of a set of harmonic oscillators in a thermal bath. Probabilities for spacetime coarse grainings are thus calculated by considering restricted density operator propagators of the quantum Brownian motion model. We also show how to achieve decoherence by replicating the system

Rosen's modelling relations via categorical adjunctions

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