Related papers: Contextual extensions of quantum gravity models
A new category of topological spaces with additional structures, called m-towers, is introduced. It is shown that there is a covariant functor which establishes a one-to-one correspondences between unital (resp. arbitrary) subhomogeneous…
A complete canonical formulation of general covariance makes it possible to construct new modified theories of gravity that are not of higher-curvature form, as shown here in a spherically symmetric setting. The usual uniqueness theorems…
We introduce contextual values as a generalization of the eigenvalues of an observable that takes into account both the system observable and a general measurement procedure. This technique leads to a natural definition of a general…
We transcribe a portion of the theory of extensions of C*-algebras to general operator algebras. We also include several new general facts about approximately unital ideals in operator algebras and the C*-algebras which they generate.
Following Crane's suggestion that categorification should be of fundamental importance in quantising gravity, we show that finite dimensional even $S^o$-real spectral triples over $\bbc$ are already nothing more than full C*-categories…
We introduce and study a purely syntactic notion of lax cones and $(\infty,\infty)$-limits on finite computads in \texttt{CaTT}, a type theory for $(\infty,\infty)$-categories due to Finster and Mimram. Conveniently, finite computads are…
General definitions for causal structures on manifolds of dimension d+1>2 are presented for the topological category and for any differentiable one. Locally, these are given as cone structures via local (pointwise) homeomorphic or…
Inclusions and extensions lie at the heart of physics and mathematics. The most relevant kind of inclusion in quantum systems is that of a von Neumann subalgebra, which is the focus of this work. We propose an object intrinsic to a given…
Contextuality has been identified as a potential resource responsible for the quantum advantage in several tasks. It is then necessary to develop a resource-theoretic framework for contextuality, both in its standard and generalized forms.…
Quantum geometric maps, which relate SU(2) spin networks and Lorentz covariant projected spin networks, are an important ingredient of spin foam models (and tensorial group field theories) for 4-dimensional quantum gravity. We give a…
We consider the extension of the general-linear and special-linear algebras by employing the Maxwell symmetry in $D$ space-time dimensions. We show how various Maxwell extensions of the ordinary space-time algebras can be obtained by a…
Recently a new impulse has been given to the experimental investigation of contextuality. In this paper we show that for a widely used definition of contextuality there can be no decisive experiment on the existence of contextuality. To…
We provide definitions for strict involutive higher categories (a vertical categorification of dagger categories), strict higher C*-categories and higher Fell bundles (over arbitrary involutive higher topological categories). We put forward…
Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K-theory of the corresponding reduced C*-algebras.…
In this article we present a review of a geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with the causal structure related to special and general relativity. We describe…
No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no-go arguments against non-contextual hidden variables. All such arguments rely on choosing special sets of quantum-mechanical…
Some quantum algebras build from deformed oscillator algebras may be described in terms of a particular case of extended umbral calculus. We give here an example of a specific relation between such certain quantum algebras and generalized…
We construct a non-contextual hidden variable model consistent with all the kinematic predictions of quantum mechanics (QM). The famous Bell-KS theorem shows that non-contextual models which satisfy a further reasonable restriction are…
A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality. The key features involve using an underlying relation rather than a function between…
This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a…