Related papers: Bohrification of local nets
Recent results by Spitters et. al. suggest that quantum phase space can usefully be regarded as a ringed topos via a process called Bohrification. They show that quantum kinematics can then be interpreted as classical kinematics, internal…
This paper shows that quantization induces a Lawvere-Tierney topology on (hence, a sheaf topos in) the quantum topos. We show that a quantization map from classical observables to self-adjoint operators on a Hilbert space naturally induces…
New foundations for quantum logic and quantum spaces are constructed by merging algebraic quantum theory and topos theory. Interpreting Bohr's "doctrine of classical concepts" mathematically, given a quantum theory described by a…
The premise of this note is the following observation: the formalism of Bohrification is a natural place for the interpretation of general non-signalling theories. We demonstrate it through an analysis of so-called box-worlds, a popular…
An observable effects a schematization of the Quantum event structure by correlating Boolean algebras picked by measurements with the Borel algebra of the real line. In a well-defined sense Boolean observables play the role of…
In integrable models of quantum field theory, local fields are normally constructed by means of the bootstrap-formfactor program. However, the convergence of their $n$-point functions is unclear in this setting. An alternative approach uses…
Quantum mechanics is able to predict challenging behaviors even in the simplest physical scenarios. These behaviors are possible because of the important dynamical role that phase plays in the evolution of quantum systems, and are very…
We describe all the localization observables of a quantum particle in a one-dimensional box in terms of sequences of unit vectors in a Hilbert space. An alternative representation in terms of positive semidefinite complex matrices is…
We study morphisms of internal locales of Grothendieck toposes externally: treating internal locales and their morphisms as sheaves and natural transformations. We characterise those morphisms of internal locales that induce surjective…
Recently, quantum entanglement has been presented as a cohomological obstruction to reconstructing a global quantum state from locally compatible information, where sheafification provides a functor that is forgetful with regards to…
When geometric quantization is applied to a manifold using a real polarization which is "nice enough", a result of Sniatycki says that the quantization can be found by counting certain objects, called Bohr-Sommerfeld leaves. Subsequently,…
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…
One of the main motivations behind so-called topos physics, as developed by Chris Isham and Andreas Doering [4-7], is to provide a framework for new theories of quantum gravity. In this article we do not search for such theories, but ask…
We define a new concept of local states in the framework of algebraic quantum field theory (AQFT). Local states are a natural generalization of states and give a clear vision of localization in the context of QFT. In terms of them, we can…
We construct a sheaf-theoretic representation of quantum observables algebras over a base category equipped with a Grothendieck topology, consisting of epimorphic families of commutative observables algebras, playing the role of local…
For any given algebra of local observables in relativistic quantum field theory there exists an associated scaling algebra which permits one to introduce renormalization group transformations and to construct the scaling (short distance)…
We show, following a previous quantization of a vacuum spherically symmetric spacetime carried out in Ref. \cite{gop}, that this setting admits a Schr\"odinger-like picture. More precisely, the technique adopted there for the definition of…
In the current debate referring to the construction of a tenable background independent theory of Quantum Gravity we introduce the notion of topos-theoretic relativization of physical representability and demonstrate its relevance…
We describe a new phenomenon in quantum cosmology: self-organised localisation. When the fundamental parameters of a theory are functions of a scalar field subject to large fluctuations during inflation, quantum phase transitions can act as…
Within the setting of algebraic quantum field theory a relation between phase-space properties of observables and charged fields is established. These properties are expressed in terms of compactness and nuclearity conditions which are the…