Automorphisms and broken symmetries in algebraic quantum field theories

1967 ◽  
Vol 47 (1) ◽  
pp. 36-48
Author(s):  
M. Guenin ◽  
G. Velo
Keyword(s):  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Broken Symmetries ◽  
Algebraic Quantum

scholarly journals Categorification of algebraic quantum field theories

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Marco Benini ◽  
Marco Perin ◽  
Alexander Schenkel ◽  
Lukas Woike
Keyword(s):  
Universal Algebra ◽  
Finite Groups ◽  
Physical Interpretation ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Algebraic Quantum

AbstractThis 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 2-category of 2AQFTs. Examples of 2AQFTs that do not come from ordinary AQFTs via this embedding are constructed by a local gauging construction for finite groups, which admits a physical interpretation in terms of orbifold theories. A categorification of Fredenhagen’s universal algebra is developed and also computed for simple examples of 2AQFTs.

scholarly journals On the Stability of KMS States in Perturbative Algebraic Quantum Field Theories

2017 ◽  
Vol 357 (1) ◽  
pp. 267-293 ◽  
Author(s):  
Nicolò Drago ◽  
Federico Faldino ◽  
Nicola Pinamonti
Keyword(s):  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Kms States ◽  
Algebraic Quantum ◽  
The Stability

scholarly journals Operads for algebraic quantum field theory

2020 ◽  
pp. 2050007
Author(s):  
Marco Benini ◽  
Alexander Schenkel ◽  
Lukas Woike
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Lorentzian Manifold ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Additional Structure ◽  
Algebraic Quantum Field Theory ◽  
Algebraic Quantum ◽  
Different Types

We construct a colored operad whose category of algebras is the category of algebraic quantum field theories. This is achieved by a construction that depends on the choice of a category, whose objects provide the operad colors, equipped with an additional structure that we call an orthogonality relation. This allows us to describe different types of quantum field theories, including theories on a fixed Lorentzian manifold, locally covariant theories and also chiral conformal and Euclidean theories. Moreover, because the colored operad depends functorially on the orthogonal category, we obtain adjunctions between categories of different types of quantum field theories. These include novel and interesting constructions such as time-slicification and local-to-global extensions of quantum field theories. We compare the latter to Fredenhagen’s universal algebra.

scholarly journals Homotopy theory of algebraic quantum field theories

2019 ◽  
Vol 109 (7) ◽  
pp. 1487-1532 ◽  
Author(s):  
Marco Benini ◽  
Alexander Schenkel ◽  
Lukas Woike
Keyword(s):  
Homotopy Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Algebraic Quantum

scholarly journals Smooth 1-Dimensional Algebraic Quantum Field Theories

2021 ◽  
Author(s):  
Marco Benini ◽  
Marco Perin ◽  
Alexander Schenkel
Keyword(s):  
Gauge Theories ◽  
Higher Dimensions ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Open Problems ◽  
Smooth Family ◽  
Algebraic Quantum ◽  
Usual Concept

AbstractThis 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 smooth family of observable algebras. Using stacks of categories, this proposal is realized concretely for the simplest case of 1-dimensional spacetimes, leading to a stack of smooth 1-dimensional AQFTs. Concrete examples of smooth AQFTs, of smooth families of smooth AQFTs and of equivariant smooth AQFTs are constructed. The main open problems that arise in upgrading this approach to higher dimensions and gauge theories are identified and discussed.

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