Related papers: Algebraic Structures in local QFT

We review QFT from the algebraic structure of its perturbative expansion and point out three new results.

This paper provides a primer in quantum field theory (QFT) based on Hopf algebra and describes new Hopf algebraic constructions inspired by QFT concepts. The following QFT concepts are introduced: chronological products, S-matrix, Feynman…

In this report I review some aspects of the algebraic structure of QFT related with the doubling of the degrees of freedom of the system under study. I show how such a doubling is related to the characterizing feature of QFT consisting in…

In this paper we investigate pointed Hopf algebras via quiver methods. We classify all possible Hopf structures arising from minimal Hopf quivers, namely basic cycles and the linear chain. This provides full local structure information for…

We show that reasonably well behaved 3d and 4D TQFts must contain certain algebraic structures. In 4D, we find both Hopf categories and trialgebras.

Conformal field theory on the half-space x>0 of Minkowski space-time ("boundary CFT") is analyzed from an algebraic point of view, clarifying in particular the algebraic structure of local algebras and the bi-localized charge structure of…

A brief survey of some aspects of noetherian Hopf algebras is given, concentrating on structure, homology, and classification, and accompanied by a panoply of open problems.

Two new approaches to numerical QFT are presented.

A method of local approximation of holomorphic solutions of algebraic equations is discussed

This short survey article reviews current understand- ing of the structure of noetherian Hopf algebras. The focus is on homological properties. A number of open problems are listed.

We present a short review of the action and coaction of Hopf algebras on Clifford algebras as an introduction to physically meaningful examples. Some q-deformed Clifford algebras are studied from this context and conclusions are derived.

We study the relationships among the various forms of the $q$ oscillator algebra and consider the conditions under which it supports a Hopf structure. We also present a generalization of this algebra together with its corresponding Hopf…

In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I will give a basic introduction to these algebras and review some occurrences in particle physics.

The aim of this paper is to show that there is a Hopf structure of the parabosonic and parafermionic algebras and this Hopf structure can generate the well known Hopf algebraic structure of the Lie algebras, through a realization of Lie…

We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of…

As Hopf truss analogues of Rota-Baxter Hopf algebras, the notion of Rota-Baxter systems of Hopf algebras is proposed. We study the relatiohship between Rota-Baxter systems of Hopf algebras and Rota-Baxter Hopf algebras, show that there is a…

The content of this paper is incorporated into hep-th/9805093

The goal of this note is to provide a constructive version of the proof of local structure of etale algebras.

Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…

In this work, the notion of a quantum inverse semigroup is introduced as a linearized generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is the natural example of a quantum inverse semigroup, several…