• Corpus ID: 246240815

Spacetimes categories and disjointness for algebraic quantum field theory

  title={Spacetimes categories and disjointness for algebraic quantum field theory},
  author={Alastair Grant-Stuart},
An algebraic quantum field theory (AQFT) may be expressed as a functor from a category of spacetimes to a category of algebras of observables. However, a generic category C whose objects admit interpretation as spacetimes is not necessarily viable as the domain of an AQFT functor; often, additional constraints on the morphisms of C must be imposed. We introduce disjointness relations, a generalisation of the orthogonality relations of Benini, Schenkel and Woike [BSW21]. In any category C… 
1 Citations

Figures from this paper

Snowmass White Paper: The Quest to Define QFT

This article provides a review of the literature on rigorous definitions and constructions in Quantum Field Theory, spanning the period of seven decades. Comparing with the ideas and constructions



The Generally Covariant Locality Principle – A New Paradigm for Local Quantum Field Theory

Abstract: A new approach to the model-independent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local

Algebraic Quantum Field Theory on Curved Spacetimes

In this chapter, we review all background material on algebraic quantum field theory on curved spacetimes which is necessary for understanding the cosmological applications discussed in the next

Homotopy theory of algebraic quantum field theories

Motivated by gauge theory, we develop a general framework for chain complex-valued algebraic quantum field theories. Building upon our recent operadic approach to this subject, we show that the

Quantum Field Theories on Categories Fibered in Groupoids

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

Conformal Generally Covariant Quantum Field Theory: The Scalar Field and its Wick Products

In this paper we generalize the construction of generally covariant quantum theories given in [BFV03] to encompass the conformal covariant case. After introducing the abstract framework, we discuss

Algebraic field theory operads and linear quantization

We generalize the operadic approach to algebraic quantum field theory [arXiv:1709.08657] to a broader class of field theories whose observables on a spacetime are algebras over any single-colored

Smooth 1-Dimensional Algebraic Quantum Field Theories

This paper proposes a refinement of the usual concept of algebraic quantum field theories (AQFTs) to theories that are smooth in the sense that they assign to every smooth family of spacetimes a

A Skeletal Model for 2d Conformal AQFTs

: A simple model for the localization of the category CLoc 2 of oriented and time-oriented globally hyperbolic conformal Lorentzian 2-manifolds at all Cauchy morphisms is constructed. This provides

Quantum Fields in Curved Spacetime: Non Global Hyperbolicity and Locality

We briefly review the current status of the algebraic approach to quantum field theory on globally hyperbolic spacetimes, both axiomatic -- for general field theories, and constructive -- for a

The existence of complete Riemannian metrics

The purpose of the present note is to prove the following results. Let M be a connected differentiable manifold which satisfies the second axiom of countability. Then (i) M admits a complete