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

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 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

Focusing on the DSE of the quark propagator (qDSE), we find a trackable truncation scheme which essentially describes a back-reaction of Goldstone bosons on the order parameter in

In Chapter 4 we improve the truncation by coupling fully dressed quark propagators back to the gluon and also include the effects of quark masses and color-superconducting