DYSON–SCHWINGER EQUATIONS AND QUANTIZATION OF GAUGE THEORIES (SUMMER ’21)

The point is that for any given quantum field theory, there always exists a Dyson-Schwinger equation, whose solution is simply related to the log-expansion of the probability

We show how to use the Hopf algebra structure of quantum field theory to derive nonperturbative results for the short-distance singular sector of a renormalizable quantum field

Hopf subalgebras of the Hopf algebra of rooted trees coming from Dyson-Schwinger equations and Lie algebras of Fa di Bruno type..

In Chapter 4 we will introduce Dyson Schwinger algebras and we will see how a relation among classical coupling constants leads to a relation among the corresponding invariant

We present the lattice structure of Feynman diagram renormalization in physical QFTs from the viewpoint of Dyson–Schwinger–Equations and the core Hopf algebra of Feynman diagrams..

We view Feynman rules as characterized by a linear and multiplicative map φ : H → A taking a Feynman graph to an element of some target algebra A of, say, smooth functions depending

Coeffients of the solution of the Dyson-Schwinger equations are translated from the Hopf algebra of rooted trees to the Hopf algebra of words.. Therein they are expressed as

In particular we relate renormalized Feynman rules φ R in this scheme to the universal property of the Hopf algebra H R of rooted trees, exhibiting a refined renormalization