Related papers: Contextual extensions of quantum gravity models
We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest,…
Starting categorically, we give simple and precise models of equivariant classifying spaces. We need these models for work in progress in equivariant infinite loop space theory and equivariant algebraic K-theory, but the models are of…
In this paper we show how the covariant gauge invariant equations for the evolution of scalar, vector and tensor perturbations for a generic $f(R)$-gravity theory can be recast in order to exploit the power of dynamical system methodology.…
We introduce a class of good endofunctors of $C^{*}$-algebras, endow it with a structure of a bimonoidal category, and define homotopies of natural transformations between such endofunctors. For every pair of $C^{*}$-algebras and a good…
The idea of treating general relativistic theories in a perturbative expansion around a topological theory has been recently put forward in the quantum gravity literature. Here we investigate the viability of this idea, by applying it to…
In this paper the authors seek to trace in an accessible fashion the rapid recent development of the theory of the matrix geometric mean in the cone of positive definite matrices up through the closely related operator geometric mean in the…
An often used model for quantum theory is to associate to every physical system a C*-algebra. From a physical point of view it is unclear why operator algebras would form a good description of nature. In this paper, we find a set of…
Certain topological invariants of the moduli space of gravitational instantons are defined and studied. Several amplitudes of two and four dimensional topological gravity are computed. A notion of puncture in four dimensions, that is…
A modification of General Relativity that is based on the gravitational Standard-Model Extension and incorporates nondynamical background fields has recently been studied via the ADM formalism. Our objective in this paper is to develop a…
Contextual type theory distinguishes between bound variables and meta-variables to write potentially incomplete terms in the presence of binders. It has found good use as a framework for concise explanations of higher-order unification,…
Considering a generalization of the Gibbons-Hawking-York covariant boundary action that depends on both the extrinsic and the intrinsic geometry of the boundary, we derive boundary conditions for the cosmological background and tensor…
We present a precise definition of extended homotopy quantum field theories and develop an orbifold construction for these theories when the target space is the classifying space of a finite group $G$, i.e. for $G$-equivariant topological…
This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a `background-free quantum theory with local…
We introduce the nuclear dimension of a C*-algebra; this is a noncommutative version of topological covering dimension based on a modification of the earlier concept of decomposition rank. Our notion behaves well with respect to inductive…
We introduce a new framework for contextuality based on simplicial sets, combinatorial models of topological spaces that play a prominent role in modern homotopy theory. Our approach extends measurement scenarios to consist of spaces…
Quantum computation can be formulated through various models, each highlighting distinct structural and resource-theoretic aspects of quantum computational power. This paper develops a unified categorical framework that encompasses these…
We give a complete $K$-theoretical description of when an extension of two simple graph $C^{*}$-algebras is again a graph $C^{*}$-algebra.
Modified gravity provides a possible explanation for the currently observed cosmic accelaration. In this paper, we study general classes of modified gravity models. The Einstein-Hilbert action is modified by using general functions of the…
In this thesis, we focus on higher-curvature extensions of Einstein gravity as toy models to probe universal properties of conformal field theory (CFT) using the gauge/gravity duality. In this context, we are particularly interested in…
An extension of the General Coordinate Transformations algebra is constructed by means geometrical consistency conditions. An class of infinite invariants is derived. In particular we construct the consistent extension of the gravitational…