The recursive counterterm procedure developed by Bogoliubov, Parasiuk, and Hepp [1], which was briefly described at the beginning of Chapter 9, yields a finite result for each Feynman diagram, order by order in perturbation theory. It is useful to interprete this procedure as an application of a R-operation to the Feynman diagram. All the finite results on higher loops in this book will be deri...

The recursive counterterm procedure developed by Bogoliubov, Parasiuk, and Hepp [1], which was briefly described at the beginning of Chapter 9, yields a finite result for each Feynman diagram, order by order in perturbation theory. It is useful to interprete this procedure as an application of a R-operation to the Feynman diagram. All the finite results on higher loops in this book will be deri...

The FDC is a general-purpose program package for Feynman Diagram Calculation. We outline previous successes in calculations and focus on its recent progress about automatic deduction the Feynman rules for first principle model, especially for the supersymmetric model, proper evaluation of the rates of multi-final-particle processes and the event generators in the SM and MSSM. A few special appl...

A brief review of recent results on analytical evaluation of double-box Feynman integrals is presented. First steps towards evaluation of massless on-shell triple-box Feynman integrals within dimensional regularization are described. The leading power asymptotic behaviour of the dimensionally regularized massless on-shell master planar triple-box diagram in the Regge limit t/s → 0 is evaluated....

The U(1) triangle anomaly is present, as an infra-red divergence, in the six-reggeon triple-regge interaction vertex obtained from a maximally non-planar Feynman diagram in the full triple-regge limit of three-to-three quark scattering.

We summarize recent results connecting multiloop Feynman diagram calculations to different parts of mathematics, with special attention given to the Hopf algebra structure of renormalization. PACS: 11.10Gh, 11.15Bt, 11.10-z, 02.90+p

Small momentum expansion of the ”sunset” diagram with three different masses is obtained. Coefficients at powers of p2 are evaluated explicitly in terms of dilogarithms and elementary functions. Also some power expansions of ”sunset” diagram in terms of different sets of variables are given. The ”sunset” diagram (see Fig. 1) was the object of investigation in several recent works [1, 2, 3, 4, 5...

Vacuum expectation values of local fields for all dual pairs of non-simply laced affine Toda field theories recently proposed are checked against perturbative analysis. The computations based on Feynman diagram expansion are performed upto two-loops. Agreement is obtained.

A framework for quantum field theory coupled to three-dimensional quantum gravity is proposed. The coupling with quantum gravity regulates the Feynman diagrams. One recovers the usual Feynman amplitudes in the limit as the cosmological constant tends to zero. The purpose of this note is to give further detail of the proposal to define a quantum field theory of particles coupled to three-dimensi...