Related papers: Recursive relations in the core Hopf algebra
We study the core Hopf algebra underlying the renormalization Hopf algebra.
We contruct here the Hopf algebra structure underlying the process of renormalization of non-commutative quantum field theory.
We provide a correspondence between one-sided coideal subrings and one-sided ideal two-sided coideals in an arbitrary bialgebroid. We prove that, under some expected additional conditions, this correspondence becomes bijective for Hopf…
Two coalgebra structures are used in quantum field theory. The first one is the coalgebra part of a Hopf algebra leading to deformation quantization. The second one is a co-module co-algebra over the first Hopf algebra and it is used to…
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 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.
We introduce two subalgebras in the type A quantum affine algebra which are coideals with respect to the Hopf algebra structure. In the classical limit q -> 1 each subalgebra specializes to the enveloping algebra U(k), where k is a fixed…
We briefly review the Hopf algebra structure arising in the renormalization of quantum field theories. We construct the Hopf algebra explicitly for a simple toy model and show how renormalization is achieved for this particular model.
The notion of Hopf center and Hopf cocenter of a Hopf algebra is investigated by the extension theory of Hopf algebras. We prove that each of them yields an exact sequence of Hopf algebras. Moreover the exact sequences are shown to satisfy…
We describe the role of Rational Hopf Algebras as the symmetries of rational field theories and discuss their relation with algebraic field theory, braided monoidal categories and modular fusion rule algebras.
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…
We investigate several Hopf algebras of diagrams related to Quantum Field Theory of Partitions and whose product comes from the Hopf algebras WSym or WQSym respectively built on integer set partitions and set compositions. Bases of these…
We review the appearance of Hopf algebras in the renormalization of quantum field theories and in the study of diffeomorphisms of the frame bundle important for index computations in noncommutative geometry.
We use a coproduct on the time-ordered algebra of field operators to derive simple relations between complete, connected and 1-particle irreducible n-point functions. Compared to traditional functional methods our approach is much more…
We introduce a new Hopf algebra that operates on pairs of finite interval partitions and permutations of equal length. This algebra captures vincular patterns, which involve specifying both the permutation patterns and the consecutive…
We study ideals in Hall algebras of monoid representations on pointed sets corresponding to certain conditions on the representations. These conditions include the property that the monoid act via partial permutations, that the…
The Hopf algebra structure underlying Feynman diagrams which governs the process of renormalization in perturbative quantum field theory is reviewed. Recent progress is briefly summarized with an emphasis on further directions of research.
We briefly review the r\^ole played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case, we analyze the noncommutative…
The quantum field algebra of real scalar fields is shown to be an example of infinite dimensional quantum group. The underlying Hopf algebra is the symmetric algebra S(V) and the product is Wick's normal product. Two coquasitriangular…
We exhibit a bijective correspondence between certain left ideal coideals in a Hopf algebroid for which the resulting quotient is a coequalizer and certain right coideal subrings which are themselves an equalizer, remarkably improving a…