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.

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 THE RELATIONS BETWEEN GENERALIZED FIELDS AND SUPERFIELDS FORMALISMS OF THE BATALIN–VILKOVISKY METHOD OF QUANTIZATION

2004 ◽  
Vol 19 (14) ◽  
pp. 2339-2353 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
General Solution ◽  
Master Equation ◽  
Gauge Theories ◽  
Relativistic Particle ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yang Mills ◽  
Topological Quantum ◽  
Topological Quantum Field Theories

A general solution of the Batalin–Vilkovisky master equation was formulated in terms of generalized fields. Recently, a superfields approach of obtaining solutions of the Batalin–Vilkovisky master equation is also established. Superfields formalism is usually applied to topological quantum field theories. However, generalized fields method is suitable to find solutions of the Batalin–Vilkovisky master equation either for topological quantum field theories or the usual gauge theories like Yang–Mills theory. We show that by truncating some components of superfields with appropriate actions, generalized fields formalism of the usual gauge theories result. We demonstrate that for some topological quantum field theories and the relativistic particle both of the methods possess the same field contents and yield similar results. Inspired by the observed relations, we give the solution of the BV master equation for on-shell N=1 supersymmetric Yang–Mills theory utilizing superfields.

scholarly journals DIFF(Σ) AND METRICS FROM HAMILTONIAN-TQFT'S IN 2+1 DIMENSIONS

1993 ◽  
Vol 08 (24) ◽  
pp. 2277-2283 ◽  
Author(s):  
ROGER BROOKS
Keyword(s):  
Topological Field Theories ◽  
Gauge Theories ◽  
Dimensional Space ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Canonical Gravity ◽  
Topological Quantum ◽  
Topological Field

The constraints of BF topological gauge theories are used to construct Hamiltonians which are anti-commutators of the BRST and anti-BRST operators. Such Hamiltonians are a signature of topological quantum field theories (TQFTs). By construction, both classes of topological field theories share the same phase spaces and constraints. We find that, for (2+1)- and (1+1)-dimensional space-times foliated as M=Σ × ℝ, a homomorphism exists between the constraint algebras of our TQFT and those of canonical gravity. The metrics on the two-dimensional hypersurfaces are also obtained.

DOES STOCHASTIC ANALYTIC REGULARIZATION PROVIDE QUANTUM FIELD THEORIES?

1992 ◽  
Vol 07 (04) ◽  
pp. 777-794
Author(s):  
C. P. MARTIN
Keyword(s):  
Field Theory ◽  
Regularization Method ◽  
Gauge Theories ◽  
Field Theories ◽  
Intermediate Step ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Point Function ◽  
Four Dimensions ◽  
Analytic Regularization

We analyze whether the so-called method of stochastic analytic regularization is suitable as an intermediate step for constructing perturbative renormalized quantum field theories. We choose a λϕ3 in six dimensions to prove that this regularization method does not in general provide a quantum field theory. This result seems to apply to any field theory with a quadratically UV-divergent stochastic two-point function, for instance λϕ4 and gauge theories in four dimensions.

Large Nf quantum field theory

2018 ◽  
Vol 33 (35) ◽  
pp. 1830032 ◽  
Author(s):  
J. A. Gracey
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Fixed Point ◽  
Critical Exponents ◽  
Gauge Theories ◽  
Historical Background ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Universal Quantum

We review the development of the large [Formula: see text] method, where [Formula: see text] indicates the number of flavours, used to study perturbative and nonperturbative properties of quantum field theories. The relevant historical background is summarized as a prelude to the introduction of the large [Formula: see text] critical point formalism. This is used to compute large [Formula: see text] corrections to [Formula: see text]-dimensional critical exponents of the universal quantum field theory present at the Wilson–Fisher fixed point. While pedagogical in part the application to gauge theories is also covered and the use of the large [Formula: see text] method to complement explicit high order perturbative computations in gauge theories is also highlighted. The usefulness of the technique in relation to other methods currently used to study quantum field theories in [Formula: see text]-dimensions is also summarized.

Zero Temperature Phase Transitions in Gauge Theories

1997 ◽  
Vol 12 (06) ◽  
pp. 1195-1203
Author(s):  
L. C. R. Wijewardhana
Keyword(s):  
Phase Transitions ◽  
Gauge Theories ◽  
Critical Value ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Temperature Phase ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Zero Temperature ◽  
Massless Fermion

Quantum field theories can exist in different phases depending on the number of massless fermion flavors they have. The vacuum structure of such a theory can be changed by varying the flavor number across a critical value. In this lecture we discuss such structure changing phase transitions in three and four dimensional gauge field theories.

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