Related papers: Algebraic Quantum Theory on Manifolds: A Haag-Kast…
We investigate up to which extend the kinematic setting of loop quantum gravity can be fit into a diffeomorphism invariant setting of algebraic QFT generalizing the Haag-Kastler setting of Wightman type QFT. The net of local (Weyl-)algebras…
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural "tangent 2-bundle," analogous to the tangent bundle…
We define a new construct in quantum field theory - the causal density matrix - obtained from the singularity structure of correlators of local operators. This object provides a necessary and sufficient condition for a quantum field theory…
All Lie bialgebra structures on the Heisenberg--Weyl algebra $[A_+,A_-]=M$ are classified and explicitly quantized. The complete list of quantum Heisenberg--Weyl algebras so obtained includes new multiparameter deformations, most of them…
The goal of this work, motivated by the desire to understand causality in classical and quantum gravity, is an in depth investigation of causality in classical field theories with quasilinear equations of motion, of which General Relativity…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved…
In this article we review our recent work on the causal structure of symmetric spaces and related geometric aspects of Algebraic Quantum Field Theory. Motivated by some general results on modular groups related to nets of von Neumann…
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…
The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly…
We provide a model independent construction of a net of C*-algebras satisfying the Haag-Kastler axioms over any spacetime manifold. Such a net, called the net of causal loops, is constructed by selecting a suitable base K encoding causal…
In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We…
A unique classification of the topological effects associated to quantum mechanics on manifolds is obtained on the basis of the invariance under diffeomorphisms and the realization of the Lie-Rinehart relations between the generators of the…
Recent research in the geometric formulation of quantum theory has implied that Weyl Geometry can be used to merge quantum theory and general relativity consistently as classical field theories. In the Weyl Geometric framework, it seems…
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional…
Based on a family of indefinite unitary representations of the diffeomorphism group of an oriented smooth $4$-manifold, a manifestly covariant $4$ dimensional and non-perturbative algebraic quantum field theory formulation of gravity is…
Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose,…
This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields…
The algebraic approach to quantum field theory focuses on the properties of local algebras, whereas the study of (possibly non-invertible) global symmetries emphasizes global aspects of the theory and spacetime. We study connections between…