All Outputs (60)

Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory (2024)
Journal Article

We construct and compare two alternative quantizations, as a time-orderable prefactorization algebra and as an algebraic quantum field theory valued in cochain complexes, of a natural collection of free BV theories on the category of m-dimensional gl... Read More about Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory.

Quantization of derived cotangent stacks and gauge theory on directed graphs (2023)
Journal Article

We study the quantization of the canonical unshifted Poisson structure on the derived cotangent stack T ∗ [X/G] of a quotient stack, where X is a smooth affine scheme with an action of a (reductive) smooth affine group scheme G. This is achieved thro... Read More about Quantization of derived cotangent stacks and gauge theory on directed graphs.

Green Hyperbolic Complexes on Lorentzian Manifolds (2023)
Journal Article

We develop a homological generalization of Green hyperbolic operators, called Green hyperbolic complexes, which cover many examples of derived critical loci for gauge-theoretic quadratic action functionals in Lorentzian signature. We define Green hyp... Read More about Green Hyperbolic Complexes on Lorentzian Manifolds.

The Linear CS/WZW Bulk/Boundary System in AQFT (2023)
Journal Article

This paper constructs in the framework of algebraic quantum field theory (AQFT) the linear Chern–Simons/Wess–Zumino–Witten system on a class of 3-manifolds M whose boundary ∂M is endowed with a Lorentzian metric. It is proven that this AQFT is equiva... Read More about The Linear CS/WZW Bulk/Boundary System in AQFT.

Strictification theorems for the homotopy time-slice axiom (2023)
Journal Article

It is proven that the homotopy time-slice axiom for many types of algebraic quantum field theories (AQFTs) taking values in chain complexes can be strictified. This includes the cases of Haag–Kastler-type AQFTs on a fixed globally hyperbolic Lorentzi... Read More about Strictification theorems for the homotopy time-slice axiom.

BV quantization of dynamical fuzzy spectral triples (2022)
Journal Article

This paper provides a systematic study of gauge symmetries in the dynamical fuzzy spectral triple models for quantum gravity that have been proposed by Barrett and collaborators. We develop both the classical and the perturbative quantum BV formalism... Read More about BV quantization of dynamical fuzzy spectral triples.

A Skeletal Model for 2d Conformal AQFTs (2022)
Journal Article

A simple model for the localization of the category CLoc2 of oriented and time-oriented globally hyperbolic conformal Lorentzian 2-manifolds at all Cauchy morphisms is constructed. This provides an equivalent description of 2-dimensional conformal al... Read More about A Skeletal Model for 2d Conformal AQFTs.

Relative Cauchy Evolution for Linear Homotopy AQFTs (2022)
Journal Article

This paper develops a concept of relative Cauchy evolution for the class of homotopy algebraic quantum field theories (AQFTs) that are obtained by canonical commutation relation quantization of Poisson chain complexes. The key element of the construc... Read More about Relative Cauchy Evolution for Linear Homotopy AQFTs.

Homotopical Analysis of 4d Chern-Simons Theory and Integrable Field Theories (2022)
Journal Article

This paper provides a detailed study of 4-dimensional Chern-Simons theory on R2× CP1 for an arbitrary meromorphic 1-form ω on CP1. Using techniques from homotopy theory, the behaviour under finite gauge transformations of a suitably regularised versi... Read More about Homotopical Analysis of 4d Chern-Simons Theory and Integrable Field Theories.

Smooth 1-Dimensional Algebraic Quantum Field Theories (2021)
Journal Article

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 smooth family of observable algebras. Using stacks of c... Read More about Smooth 1-Dimensional Algebraic Quantum Field Theories.

Batalin–Vilkovisky quantization of fuzzy field theories (2021)
Journal Article

We apply the modern Batalin–Vilkovisky quantization techniques of Costello and Gwilliam to noncommutative field theories in the finite-dimensional case of fuzzy spaces. We further develop a generalization of this framework to theories that are equiva... Read More about Batalin–Vilkovisky quantization of fuzzy field theories.

Classical BV formalism for group actions (2021)
Journal Article

We study the derived critical locus of a function f: [X/G] → 1 on the quotient stack of a smooth affine scheme X by the action of a smooth affine group scheme G. It is shown that dCrit(f) R [Z/G] is a derived quotient stack for a derived affine schem... Read More about Classical BV formalism for group actions.

Categorification of algebraic quantum field theories (2021)
Journal Article

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 2-category... Read More about Categorification of algebraic quantum field theories.

Dirac operators on noncommutative hypersurfaces (2020)
Journal Article

© 2020 Elsevier B.V. This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures f... Read More about Dirac operators on noncommutative hypersurfaces.

Operads for algebraic quantum field theory (2020)
Journal Article

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 addit... Read More about Operads for algebraic quantum field theory.

On the relationship between classical and deformed Hopf fibrations (2020)
Journal Article

The ?-deformed Hopf fibration S3??S2 over the commutative 2-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated module functors and that the affine spaces of clas... Read More about On the relationship between classical and deformed Hopf fibrations.

Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory (2020)
Journal Article

We provide an elegant homological construction of the extended phase space for linear Yang-Mills theory on an oriented and time-oriented Lorentzian manifold M with a time-like boundary @M that was proposed by Donnelly and Freidel [JHEP 1609, 102 (201... Read More about Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory.

Cheeger-Simons differential characters with compact support and Pontryagin duality (2019)
Journal Article
Becker, C., Benini, M., Schenkel, A., & Szabo, R. J. (2019). Cheeger-Simons differential characters with compact support and Pontryagin duality. Communications in Analysis and Geometry, 27(7), 1473–1522

By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact... Read More about Cheeger-Simons differential characters with compact support and Pontryagin duality.

Linear Yang–Mills Theory as a Homotopy AQFT (2019)
Journal Article

It is observed that the shifted Poisson structure (antibracket) on the solution complex of Klein–Gordon and linear Yang–Mills theory on globally hyperbolic Lorentzian manifolds admits retarded/advanced trivializations (analogs of retarded/advanced Gr... Read More about Linear Yang–Mills Theory as a Homotopy AQFT.

Model-independent comparison between factorization algebras and algebraic quantum field theory on Lorentzian manifolds (2019)
Journal Article

This paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic Lorentzian manifolds. Functorial constructions that map between these two types of theories in both directions are dev... Read More about Model-independent comparison between factorization algebras and algebraic quantum field theory on Lorentzian manifolds.