Feynman graph generation and calculations in the Hopf algebra of Feynman graphs

Abstract

Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang-Mills, QED and ${\phi }^k$ theories. Using dedicated graph theoretic tools feyngen can generate graphs of comparatively high loop orders. feyncop implements the Hopf algebra of those Feynman graphs which incorporates the renormalization procedure necessary to calculate finite results in perturbation theory of the underlying quantum field theory. feyngen is validated by comparison to explicit calculations of zero dimensional quantum field theories and feyncop is validated using a combinatorial identity on the Hopf algebra of graphs.

16 pages

References in corpus (4)

• The massless higher-loop two-point function
• Renormalization of gauge fields: A Hopf algebra approach
• On the analytic computation of massless propagators in dimensional regularization
• Quantization of gauge fields, graph polynomials and graph cohomology

Cited by in corpus (19)

• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Numbers and Functions in Quantum Field Theory
• Collider Physics at the Precision Frontier
• Tropical Monte Carlo quadrature for Feynman integrals
• Renormalized asymptotic enumeration of Feynman diagrams
• The Hopf algebra structure of the $R^{\ast }$-operation
• Recursive computation of Feynman periods
• Algebraic lattices in QFT renormalization
• Flow-oriented perturbation theory
• Gauge Symmetries and Renormalization
• Log-Expansions from Combinatorial Dyson-Schwinger Equations
• Renormalization in combinatorially non-local field theories: the Hopf algebra of 2-graphs
• Hopf-algebraic Renormalization of QED in the linear covariant Gauge
• Algebraic Structures in the Coupling of Gravity to Gauge Theories
• Algebraic Interplay between Renormalization and Monodromy
• Phi4tools: Compilation of Feynman diagrams for Landau-Ginzburg-Wilson theories
• Filtrations in Dyson-Schwinger equations: next-to^{j} -leading log expansions systematically
• Computations and generation of elements on the Hopf algebra of Feynman graphs
• A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory