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

DYSON-SCHWINGER EQUATIONS IN TERMS OF RANDOM WALKS: FOUR-FERMION INTERACTIONS

1993 ◽  
Vol 08 (27) ◽  
pp. 4915-4935
Author(s):  
T. JAROSZEWICZ ◽  
P.S. KURZEPA
Keyword(s):  
Random Walks ◽  
Physical Interpretation ◽  
Equations Of Motion ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Coupling Constant ◽  
Gap Equation ◽  
Starting Point ◽  
Bare Coupling Constant

Quantum field theories of interacting fermions have been recently formulated in terms of directed random walks. Using this formulation, we derive a hierarchy of equations for the correlation functions of scalar N-component four-fermion theories. These follow from an analysis of the underlying random process, and from geometric considerations. Our equations are, as we show, equivalent to the standard Dyson-Schwinger equations of motion, and are a convenient starting point for nonperturbative investigations of four-fermion theories. In particular, we discuss the physical interpretation of the gap equation in the language of random walks, and show that, in both the N→0 and N→∞ limits, an interacting theory can be obtained only for a finely tuned negative bare coupling constant.

TOPOLOGICAL QUANTUM FIELD THEORIES ASSOCIATED TO FINITE GROUPS AND CROSSED G-SETS

1992 ◽  
Vol 01 (01) ◽  
pp. 1-20 ◽  
Author(s):  
DAVID N. YETTER
Keyword(s):  
Gauge Group ◽  
Quantum Groups ◽  
Finite Groups ◽  
Gauge Theories ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Link Invariants ◽  
Topological Quantum ◽  
Topological Quantum Field Theories

Using methods suggested by the work of Turaev and Viro [11, 12], we provide a detailed construction of topological quantum field theories associated to finite crossed G-sets. Our construction of theories associated to finite groups fills in some details implicit in Dijkgraaf and Witten's [3] discussion of topological gauge theories with finite gauge group, while the theories associated to finite crossed G-sets simultaneously extend Dijkgraaf and Witten's [3] results to 3-manifolds equipped with links and Freyd and Yetter's [5] construction of link invariants from crossed G-sets from links in the 3-sphere to links in arbitrary 3-manifolds. Topological interpretations of the manifold and link invariants associated to these TQFT's are provided. We conclude discussion of our results as a toy model for QFT and of their relation to quantum groups.

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 The Bethe ansatz and the Tzitzéica–Bullough–Dodd equation

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120052 ◽  
Author(s):  
Patrick Dorey ◽  
Simone Faldella ◽  
Stefano Negro ◽  
Roberto Tateo
Keyword(s):  
Bethe Ansatz ◽  
Nonlinear Wave ◽  
Physical Interpretation ◽  
Wave Equations ◽  
Field Theories ◽  
Nonlinear Wave Equations ◽  
Infinite Cylinder ◽  
Quantum Field Theories ◽  
Quantum Field

The theory of classically integrable nonlinear wave equations and the Bethe ansatz systems describing massive quantum field theories defined on an infinite cylinder are related by an important mathematical correspondence that still lacks a satisfactory physical interpretation. In this paper, we shall extend this link to the case of the classical and quantum versions of the Tzitzéica–Bullough–Dodd model.

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