On the Hopf Algebra Structure of Perturbative Quantum Eld Theories

On the Hopf algebra structure of perturbative quantum field theories

We show that the process of renormalization encapsules a Hopf algebra structure in a natural manner. This sheds light on the recently proposed connection between knots and renormalization theory.

Dyson Schwinger Equations: From Hopf algebras to Number Theory

We consider the structure of renormalizable quantum field theories from the viewpoint of their underlying Hopf algebra structure. We review how to use this Hopf algebra and the ensuing Hochschild cohomology to derive non-perturbative results for the short-distance singular sector of a renormalizable quantum field theory. We focus on the short-distance behaviour and thus discuss renormalized Gre...

Hopf algebra approach to Feynman diagram calculations

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.

Using the Hopf algebra structure of QFT in calculations

We employ the recently discovered Hopf algebra structure underlying perturbative Quantum Field Theory to derive iterated integral representations for Feynman diagrams. We give two applications: to massless Yukawa theory and quantum electrodynamics in four dimensions. 11.10.Gh, 11.15.Bt Typeset using REVTEX 1

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras