Using the Hopf Algebra Structure of QFT in Calculations

Abstract

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.

28 p, Revtex, epsf for figures, minor changes, to appear in Phys.Rev.D

References in corpus (5)

• Hopf Algebras, Renormalization and Noncommutative Geometry
• On Overlapping Divergences
• A geometrical angle on Feynman integrals
• Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links
• Counting planar diagrams with various restrictions

Cited by in corpus (19)

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• Hopf algebra approach to Feynman diagram calculations
• Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Pade-Borel resummation
• Shuffle relations for regularised integrals of symbols
• The Hopf algebra of Feynman graphs in QED
• Is Quantum Spacetime Infinite Dimensional ?
• Combinatorics of (perturbative) quantum field theory
• An algebraic approach to coarse graining
• New mathematical structures in renormalizable quantum field theories
• Matrix Representation of Renormalization in Perturbative Quantum Field Theory
• Non-Linear Algebra and Bogolubov's Recursion
• On the Invariance of Residues of Feynman Graphs
• On the Connes-Moscovici Hopf algebra associated to the diffeomorphisms of a manifold
• Leading RG logs in ${\varphi }^4$ theory
• Feynman Diagrams and Lax Pair Equations
• Introduction to Hopf algebras in renormalization and noncommutative geometry
• Hopf algebra and renormalization: A brief review
• Riemann-Hilbert Problem and Quantum Field Theory: Integrable Renormalization, Dyson-Schwinger Equations
• Simply Generated Trees, B-series and Wigner Processes