Related papers: A quantum field comonad
In this paper we try to define the higher dimensional analogues of vertex algebras. In other words we define algebras which we hope have the same relation to higher dimensional quantum field theories that vertex algebras have to one…
The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
We aim to explore if inside a quantum vertex algebras, we can find the right notion of a quantum conformal algebra.
A definition of a quantum vertex algebra, which is a deformation of a vertex algebra, was proposed by Etingof and Kazhdan in 1998. In a nutshell, a quantum vertex algebra is a braided state-field correspondence which satisfies associativity…
We propose an extension of the definition of vertex algebras in arbitrary space-time dimensions together with their basic structure theory. An one-to-one correspondence between these vertex algebras and axiomatic quantum field theory (QFT)…
We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.
This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields…
The free algebra adjunction, between the category of algebras of a monad and the underlying category, induces a comonad on the category of algebras. The coalgebras of this comonad are the topic of study in this paper (following earlier…
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…
The notion of vertex operator coalgebra is presented and motivated via the geometry of conformal field theory. Specifically, we describe the category of geometric vertex operator coalgebras, whose objects have comultiplicative structures…
We introduce the notion of vertex coalgebra, a generalization of vertex operator coalgebras. Next we investigate forms of cocommutativity, coassociativity, skew-symmetry, and an endomorphism, $D^*$, which hold on vertex coalgebras. The…
A field algebra is a ``non-commutative'' generalization of a vertex algebra. In this paper we develop foundations of the theory of field algebras.
A superfield formalism for quantum fields with N-extended superconformal symmetry is developed using vertex algebra techniques in four dimensions.
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
We provide a short introduction to the main features of the algebraic approach to quantum field theories.
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…
We give an account of the current state of the approch to quantum field theory via Hopf algebras and Hochschild cohomology. We emphasize the versatility and mathematical foundation of this algebraic structure, and collect algebraic…
In this review we report on how the problem of general covariance is treated within the algebraic approach to quantum field theory by use of concepts from category theory. Some new results on net cohomology and superselection structure…
Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations,…