A new version of the Feynman graph plotting tool JaxoDraw is presented. Version 2.0 is a fundamental rewrite of most of the JaxoDraw core and some functionalities, in particular importing graphs, are not backward-compatible with the 1.x branch. The most prominent new features include: drawing of Bézier curves for all particle modes, on-the-fly update of edited objects, multiple undo/redo functi...

It was recently shown that the renormalization of quantum field theory is organized by the Hopf algebra of decorated rooted trees, whose coproduct identifies the divergences requiring subtraction and whose antipode achieves this. We automate this process in a few lines of recursive symbolic code, which deliver a finite renormalized expression for any Feynman diagram. We thus verify a representa...

The work presented in this paper has been motivated by a reconsideration of photon-photon scattering, generalized to arbitrary dimensional spacetime [1] and to any number of scattering photons. Though an extremely feeble process and therefore very difficult to observe, this nonlinear process of scattering photons by photons has attracted considerable attention [2, 3, 4, 5, 6, 7, 8] since Euler ...

The physical motivations have been discussed extensively in the reports of the recent years. Thus, we only would like to mention that the problems treated within this project aim for the evaluation of so-called Feynman diagrams which in turn lead to quantum corrections within a given quantum field theory like Quantum Electrodynamics or Quantum Chromodynamics but also supersymmetric theories. Am...

So far, we have considered only a single real field φ with a φ 4-interaction. The theory can, however, easily be extended to a set of N identical real fields φ α with α = 1,. .. , N. This extension does not produce any new Feynman diagrams. Additional work arises from the fact that the coupling constant g becomes now a tensor g αβγδ , and each momentum integral in a Feynman diagram is accompani...

It was recently shown that the renormalization of quantum eld theory is organized by the Hopf algebra of decorated rooted trees, whose coproduct identiies the divergences requiring subtraction and whose antipode achieves this. We automate this process in a few lines of recursive symbolic code, which deliver a nite renormalized expression for any Feynman diagram. We thus verify a representation ...

where D is a partition of {1 . . . n} into 4 nonempty sets, P i is the sum of momenta in i ∈ D and D0 a scalar box. In other words, scalar one-loop integrals (up to boxes) form a basis. Thus, coefficients in the expansion (BD etc.) are uniquely determined, although some reduction method can be more efficient than others. However, troublesome points where the numerical stability of the result is...

We investigate numerically and analytically Potts models on " thin " random graphs – generic Feynman diagrams, using the idea that such models may be expressed as the N → 1 limit of a matrix model. The thin random graphs in this limit are locally tree-like, in distinction to the " fat " random graphs that appear in the planar Feynman diagram limit, N → ∞, more familiar from discretized models o...