Related papers: Renormalized Schwinger-Dyson functional
In perturbative SU(N) Chern-Simons gauge theory, it is shown that the Schwinger-Dyson equations assume a quite simplified form. The generating functional of the correlation functions of the curvature is considered; it is demonstrated that…
We consider a superrenomalizable gauge theory of topological type, in which the structure group is equal to the inhomogeneous group ISU(2). The generating functional of the correlation functions of the gauge fields is derived and its…
Using functional derivatives with respect to free propagators and interactions we derive a closed set of Schwinger-Dyson equations in quantum electrodynamics. Its conversion to graphical recursion relations allows us to systematically…
We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A…
The chirally rotated Schr\"odinger functional ($\chi$SF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schr\"odinger functional (SF), with different lattice symmetries and a common continuum limit…
The critical dynamics of the chiral symmetry breaking induced by gauge interaction is examined in the Wilson renormalization group framework in comparison with the Schwinger-Dyson approach. We derive the beta functions for the four-fermi…
We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not…
In this expository article we review recent advances in our understanding of the combinatorial and algebraic structure of perturbation theory in terms of Feynman graphs, and Dyson-Schwinger equations. Starting from Lie and Hopf algebras of…
The Schwinger equations of QED are rewritten in three different ways as integral equations involving functional derivatives, which are called weak field, strong field, and SCF quantum electrodynamics. The perturbative solutions of these…
We present a general formalism that allows for the computation of large-order renormalized expansions in the spacetime representation, effectively doubling the numerically attainable perturbation order of renormalized Feynman diagrams. We…
The general normal ordering problem for boson strings is a combinatorial problem. In this note we restrict ourselves to single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, such as…
We present a non-perturbative formulation of renormalization by viewing the regularized Schwinger-Dyson hierarchy as a meromorphic connection, that is, as a D-module on the product of spacetime with the regulator disc. The irregular…
We study Chern-Simons Gauge Theory in axial gauge on ${\mathbb R}^3.$ This theory has a quadratic Lagrangian and therefore expectations can be computed nonperturbatively by explicit formulas, giving an (unbounded) linear functional on a…
I review the way the many-body Green functions are used to renormalize the perturbation theory of correlated fermions. The Green functions are introduced to implement systematically dynamical corrections to the static mean-field theory. The…
The aim of this paper is to describe how to use regularization and renormalization to construct a perturbative quantum field theory from a Lagrangian. We first define renormalizations and Feynman measures, and show that although there need…
Using functional derivatives with respect to the free correlation function we derive a closed set of Schwinger-Dyson equations in phi^4-theory. Its conversion to graphical recursion relations allows us to systematically generate all…
The generating functional for scalar theories admits a representation which is dual with respect to the one introduced by Schwinger, interchanging the role of the free and interacting terms. It maps $\int V(\delta_J)$ and $J\Delta J$ to…
The consistent description of unstable particles, renormalons, or other Schwinger--Dyson-type of solutions within the framework of perturbative gauge field theories necessitates the definition and resummation of off-shell Green's functions,…
We propose a numerical method for resummation of perturbative series, which is based on the stochastic perturbative solution of Schwinger-Dyson equations. The method stochastically estimates the coefficients of perturbative series, and…
We derive the existence of Hopf subalgebras generated by Green's functions in the Hopf algebra of Feynman graphs of a quantum field theory. This means that the coproduct closes on these Green's functions. It allows us for example to derive…