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

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  • Anastasios Mallios
  • Elias Zafiris

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.

Suggested Citation

  • Anastasios Mallios & Elias Zafiris, 2011. "The Homological Kähler-de Rham Differential Mechanism: II. Sheaf-Theoretic Localization of Quantum Dynamics," Advances in Mathematical Physics, Hindawi, vol. 2011, pages 1-13, July.
    • Handle: RePEc:hin:jnlamp:189801
    DOI: 10.1155/2011/189801
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