Related papers: Algebraic field theory operads and linear quantiza…
In these proceedings we summarize previous work where we formalize a general concept of algebraic field theories using operads. After giving a gentle reminder of algebraic quantum field theory, operads and their algebras, we construct field…
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…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
A brief overview of the recent developments of operadic and higher categorical techniques in algebraic quantum field theory is given. The relevance of such mathematical structures for the description of gauge theories is discussed.
Algebraic operads provide a powerful tool to understand the homotopy theory of the types of (co)algebras they encode. So far, the principal results and methods that this theory provides were only available in characteristic zero. The reason…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
In this paper we define and compare several new Quillen model structures which present the homotopy theory of algebraic quantum field theories. In this way, we expand foundational work of Benini et al. by providing a richer framework to…
Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
This chapter provides a non-technical overview and motivation for the recent interactions between algebraic quantum field theory (AQFT) and rather abstract mathematical disciplines such as operads, model categories and higher categories.
Algebraic quantum field theory and prefactorization algebra are two mathematical approaches to quantum field theory. In this monograph, using a new coend definition of the Boardman-Vogt construction of a colored operad, we define homotopy…
We verify that certain algebras appearing in string field theory are algebras over Feynman transform of modular operads which we describe explicitly. Equivalent description in terms of solutions of generalized BV master equations are…
We demonstrate how one can see quantization of geometry, and quantum algebraic structure in supersymmetric gauge theory.
This text, based on the author's Bachelor's thesis, introduces the theory of Algebraic Operads, a mathematical formalism that provides a unifying framework for modern algebra. We demonstrate how the fundamental theories of associative,…
We provide a short introduction to the main features of the algebraic approach to quantum field theories.
It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…
Motivated by gauge theory, we develop a general framework for chain complex valued algebraic quantum field theories. Building upon our recent operadic approach to this subject, we show that the category of such theories carries a canonical…
We apply the theory of operadic Koszul duality to provide a cofibrant resolution of the colored operad whose algebras are prefactorization algebras on a fixed space M. his allows us to describe a notion of prefactorization algebra up to…