Independence Conditions for Nets of Local Algebras as Sheaf Conditions
arXiv:1309.5639
Abstract
We apply constructions from topos-theoretic approaches to quantum theory to algebraic quantum field theory. Thus a net of operator algebras is reformulated as a functor that maps regions of spacetime into a category of ringed topoi. We ask whether this functor is a sheaf, a question which is related to the net satisfying certain kinematical independence conditions. In addition, we consider a C*-algebraic version of Nuiten's recent sheaf condition, and demonstrate how it relates to C*-independence of the underlying net of operator algebras.
34 pages, 0 figures
References in corpus (6)
- A Topos Foundation for Theories of Physics: I. Formal Languages for Physics
- A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory
- A Topos Foundation for Theories of Physics: IV. Categories of Systems
- A Topos Foundation for Theories of Physics: III. The Representation of Physical Quantities With Arrows
- The Cohomology of Non-Locality and Contextuality
- Bohrification of local nets of observables