Related papers: Tadpole Summation by Dyson-Schwinger Equations
General formula for symmetry factors (S-factor) of Feynman diagrams containing fields with high spins is derived. We prove that symmetry factors of Feynman diagrams of well-known theories do not depend on spins of fields. In contributions…
Matrix field theory is a combinatorially non-local field theory which has recently been found to be a non-trivial but solvable QFT example. To generalize such non-perturbative structures to other models, a more combinatorial understanding…
We calculate the complete tadpoles and self-energies at the two-loop order for scalars in general renormalisable theories, a crucial component for calculating two-loop electroweak corrections to Higgs-boson masses or for any scalar beyond…
This is a simple mathematical introduction into Feynman diagram technique, which is a standard physical tool to write perturbative expansions of path integrals near a critical point of the action. I start from a rigorous treatment of a…
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…
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…
It has been recently shown that a certain non-topological spin foam model can be obtained from the Feynman expansion of a field theory over a group. The field theory defines a natural ``sum over triangulations'', which removes the cut off…
Two examples of recent progress in applications of the Dyson-Schwinger equation (DSE) formalism are presented: (1) Strong coupling quantum electrodynamics in 4 dimensions (QED$_4$) is an often studied model, which is of interest both in its…
Supersymmetric gauge theories are characterized by the existence of a transformation of the bosonic fields (Nicolai map) such that the Jacobi determinant of the transformation equals the product of the Matthews-Salam-Seiler and…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
We formulate scalar field theories in a curved braided $L_\infty$-algebra formalism and analyse their correlation functions using Batalin-Vilkovisky quantization. We perform detailed calculations in cubic braided scalar field theory up to…
We develop a new representation for the integrals associated with Feynman diagrams. This leads directly to a novel method for the numerical evaluation of these integrals, which avoids the use of Monte Carlo techniques. Our approach is based…
In these lectures we present a general introduction to topological quantum field theories. These theories are discussed in the framework of the Mathai-Quillen formalism and in the context of twisted N=2 supersymmetric theories. We discuss…
Gauge theories have been a cornerstone of the description of the world at the level of the fundamental particles. The Lagrangian or the action describing the corresponding interactions is invariant under certain gauge transformations. This…
A concise survey is given of the general method of reduction in the number of coupling parameters. Theories with several independent couplings are related to a set of theories with a single coupling. The reduced theories may or may not have…
The answers for Feynman diagrams satisfy various kinds of differential equations -- which is not a surprise, because they are defined as Gaussian correlators, possessing a vast variety of Ward identities and superintegrability properties.…
We describe various expansion schemes that can be used to study gravitational clustering. Obtained from the equations of motion or their path-integral formulation, they provide several perturbative expansions that are organized in different…
We investigate the quantum structure of Witten's cubic open bosonic string field theory by computing the one-loop contribution to the open string tadpole using both oscillator and conformal field theory methods. We find divergences and a…
Gauge theories appear broadly in physics, ranging from the standard model of particle physics to long-wavelength descriptions of topological systems in condensed matter. However, systems with sign problems are largely inaccessible to…
We propose that perturbative quantum field theory and string theory can be consistently modified in the infrared to eliminate, in a radiatively stable manner, tadpole instabilities that arise after supersymmetry breaking. This is achieved…