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

The propagators then satisfy a system of equations involving the insertion operators, called systems of Dyson-Schwinger equations... We here assume that f is

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

The free dendrifrom algebra on one gener- ator is described in Loday and Ronco [1998] in terms of planar binary trees, obtaining a Hopf algebra on these objects known as the

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