We construct a canonical transformation that takes the usual Yang-Mills action into one whose Feynman diagram expansion generates the MHV rules. The offshell continuation appears as a natural consequence of using light-front quantisation surfaces. The construction extends to include massless fermions.

The string-inspired technique is used for a first calculation of the one-loop axialvector vacuum polarisation in a general constant electromagnetic field. A compact result is reached for the difference between this tensor and the corresponding vector vacuum polarisation. This result is confirmed by a Feynman diagram calculation. Its physical relevance is briefly discussed.

This expository article is an expanded version of the talk given by the author at the 2013 ICCM conference in Taipei. We report our recent work on explicit closed formulas of the asymptotic expansions of the Bergman kernel, and the relationship to deformation quantization on Kähler manifolds. These formulas are expressed as summations over strongly connected graphs.

A 3-dimensional model dual to the Rozansky-Witten topological sigma-model with a hyper-Kähler target space is considered. It is demonstrated that a Feynman diagram calculation of the classical part of its partition function yields the Milnor linking number.

Co-operation of the Feynman DIagram ANAlyzer (DIANA) with the underlying operational system (UNIX) is presented. We discuss operators to run external commands and a recent development of parallel processing facilities and an extension in the spirit of a component model.

A 3-dimensional model dual to the Rozansky-Witten topological sigma-model with a hyper-Kähler target space is considered. It is demonstrated that a Feynman diagram calculation of the classical part of its partition function yields the Milnor linking number.

We present a review of the Bielefeld-Dubna activities on the multiloop calculations. In the first part a C-program DIANA (DIagram ANAlyser) for the automation of Feynman diagram evaluations is presented, in the second part various techniques for the evaluation of scalar diagrams are described, based on the Taylor expansion method and large mass expansion. 1. Automation of Feynman diagram evalua...

We present an application that automatically writes the Helas library corresponding to the Feynman rules of any Lagrangian, renormalizable or not, in quantum field theory. The code, written in Python, takes the Universal FeynRules Output (Ufo) as an input and produces the complete set of routines (wavefunctions and amplitudes) that are needed for the computation of Feynman diagrams at leading a...

We compare the Bakamjian-Thomas (BT) formulation of relativistic few-body systems with light front field theories that maintain closer contact with Feynman diagrams. We find that Feynman diagrams distinguish Melosh rotations and other kinematical quantities belonging to various composite subsystem frames that correspond to different loop integrals. The BT formalism knows only the rest frame of ...

Using a Mellin-Barnes representation, we compute the on-shell massless planar double box Feynman diagram with an irreducible scalar product of loop momenta in the numerator. This diagram is needed in calculations of two loop corrections to scattering processes of massless particles, together with the double box without numerator calculated previously by Smirnov. We verify the poles in of our re...