About this Journal Submit a Manuscript Table of Contents
Advances in Mathematical Physics
Volume 2011 (2011), Article ID 189801, 13 pages
http://dx.doi.org/10.1155/2011/189801
Research Article

The Homological Kähler-de Rham Differential Mechanism: II. Sheaf-Theoretic Localization of Quantum Dynamics

Department of Mathematics, University of Athens, Panepistimioupolis, 15784 Athens, Greece

Received 7 March 2011; Accepted 30 May 2011

Academic Editor: Mauro Francaviglia

Copyright © 2011 Anastasios Mallios and Elias Zafiris. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The homological Kähler-de Rham differential mechanism models the dynamical behavior of physical fields by purely algebraic means and independently of any background manifold substratum. This is of particular importance for the formulation of dynamics in the quantum regime, where the adherence to such a fixed substratum is problematic. In this context, we show that the functorial formulation of the Kähler-de Rham differential mechanism in categories of sheaves of commutative algebras, instantiating generalized localization environments of physical observables, induces a consistent functorial framework of dynamics in the quantum regime.