Operads for algebraic quantum field theory

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Operads for algebraic quantum field theory. / Benini, Marco; Schenkel, Alexander; Woike, Lukas.

In: Communications in Contemporary Mathematics, Vol. 23, No. 02, 2050007, 2021.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Benini, M, Schenkel, A & Woike, L 2021, 'Operads for algebraic quantum field theory', Communications in Contemporary Mathematics, vol. 23, no. 02, 2050007. https://doi.org/10.1142/S0219199720500078

APA

Benini, M., Schenkel, A., & Woike, L. (2021). Operads for algebraic quantum field theory. Communications in Contemporary Mathematics, 23(02), [2050007]. https://doi.org/10.1142/S0219199720500078

Vancouver

Benini M, Schenkel A, Woike L. Operads for algebraic quantum field theory. Communications in Contemporary Mathematics. 2021;23(02). 2050007. https://doi.org/10.1142/S0219199720500078

Author

Benini, Marco ; Schenkel, Alexander ; Woike, Lukas. / Operads for algebraic quantum field theory. In: Communications in Contemporary Mathematics. 2021 ; Vol. 23, No. 02.

Bibtex

@article{06cc218087844fc79b67149b8c58e59e,
title = "Operads for algebraic quantum field theory",
abstract = "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{\textquoteright}s universal algebra.",
author = "Marco Benini and Alexander Schenkel and Lukas Woike",
year = "2021",
doi = "10.1142/S0219199720500078",
language = "English",
volume = "23",
journal = "Communications in Contemporary Mathematics",
issn = "0219-1997",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "02",

}

RIS

TY - JOUR

T1 - Operads for algebraic quantum field theory

AU - Benini, Marco

AU - Schenkel, Alexander

AU - Woike, Lukas

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

U2 - 10.1142/S0219199720500078

DO - 10.1142/S0219199720500078

M3 - Journal article

VL - 23

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

SN - 0219-1997

IS - 02

M1 - 2050007

ER -

ID: 249497469