Insertion and Elimination Lie Algebra: the Ladder case

Abstract

We prove that insertion-elimination Lie algebra of Feynman graphs, in the ladder case, has a natural interpretation in terms of a certain algebra of infinite dimensional matrices. We study some aspects of its representation theory and we discuss some relations with the representation of the Heisenberg algebra

LaTex, 17 pages, typos corrected, to appear in LMP

References in corpus (4)

• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• Renormalization in quantum field theory and the Riemann-Hilbert problem II: the $\beta$-function, diffeomorphisms and the renormalization group
• Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality
• Insertion and Elimination: the doubly infinite Lie algebra of Feynman graphs

Cited by in corpus (11)

• Integrable Renormalization II: the general case
• Hopf algebra approach to Feynman diagram calculations
• From Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory
• Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field Theory
• Integrable Renormalization I: the Ladder Case
• Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees
• The Structure of the Ladder Insertion-Elimination Lie algebra
• What is the trouble with Dyson--Schwinger equations?
• On the structure and representations of the insertion-elimination Lie algebra
• Automorphisms and derivations of the insertion-elimination algebra and related graded Lie algebras
• Riemann-Hilbert Problem and Quantum Field Theory: Integrable Renormalization, Dyson-Schwinger Equations