Related papers: Quantum Fields as Category Algebras
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the…
The purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory,…
This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…
We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
Quantum field theory (QFT) on fractal spacetimes is a program aiming at quantizing the gravitational interaction consistently at all energy scales thanks to an intrinsically or dynamically induced multiscale or multifractal-like spacetime…
Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may…
We encapsulate the basic notions of the theory of vertex algebras into the construction of a comonad on an appropriate category of formal distributions. Vertex algebras are recovered as coalgebras over this comonad.
In this review we report on how the problem of general covariance is treated within the algebraic approach to quantum field theory by use of concepts from category theory. Some new results on net cohomology and superselection structure…
Despite its name, Quantum Field Theory (QFT) has been built to describe interactions between localizable particles. For this reason the actual formalism of QFT is partly based on a suitable generalization of the one already used for systems…
Quantum Field Theory (QFT) developed in Rindler space-time and its thermal properties are analyzed by means of quantum groups approach. The quantum deformation parameter, labelling the unitarily inequivalent representations, turns out to be…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link…
We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the…