A Feynman diagram is a graphical construction that describes certain interactions in physics. Most calculations with such diagrams reduce to consideration of connected Feynman diagrams. These in turn may be constructed from line-irreducible Feynman diagrams, those for which removal of a single line does not destroy connectivity. The purpose of this article is to exhibit the combinatorial nature...

A new algorithm for the automatic computa.tion of Feynman diagram amplitudes in quantum field theory is presented. Once the topology of a diagram is defined, the algorithm constructs all corresponding light-cone time-orderings. We explore the method for twoand three-loop calculations in QED. Submitted to Journal of Computational Physics * Supported in part by the Department of energy under cont...

When loop momenta of a Feynman or a nonabelian cut diagram are written in lightcone coordinates, integration over their + components can be performed using residue calculus. This yields a number of terms, in which the + components of their internal momenta are evaluated at the poles of appropriate internal lines. The challenge is to find these internal lines for an arbitrarily complicated multi...

(a) Draw the Feynman diagram which gives the leading contribution to the process φφ→ φφ. (b) Derive the correct sign of the amplitude by considering the relevant matrix elements of powers of the interaction hamiltonian. (c) Evaluate the diagram in terms of a spinor trace and a momentum integral. Do not do the momentum integral. Suppose that the integral is cutoff at large k by some cutoff Λ. Es...

Our aim is to put the partially successful analytic noncovariant approaches to Coulomb gauge QCD on a firm and systematic basis. To this end, we develop a generating functional approach to the equal-time correlation functions. In fact, such a functional is given in terms of the vacuum wave functional, however, in a perturbative expansion of the equal-time correlation functions, the vacuum wave ...

Perturbative quantum field theory for the Ising model at the three-loop level yields a tetrahedral Feynman diagram C(a, b) with masses a and b and four other lines with unit mass. The completely symmetric tetrahedron CTet ≡ C(1, 1) has been of interest from many points of view, with several representations and conjectures having been given in the literature. We prove a conjectured exponentially...

This paper explores the idea that within the framework of threedimensional quantum gravity one can extend the notion of Feynman diagram to include the coupling of the particles in the diagram with quantum gravity. The paper concentrates on the non-trivial part of the gravitational response, which is to the large momenta propagating around a closed loop. By taking a limiting case one can give a ...

The effective QCD Hamiltonian is constructed with the help of the background perturbation theory, and relativistic Feynman–Schwinger path integrals for Green's functions. The resulting spectrum displays mass gaps of the order of one GeV, when additional valence gluon is added to the bound state. Mixing between meson, hybrid, and glueball states is defined in two ways: through generalized Green'...

New developments concerning the extension of the recently introduced (1) Feynman diagram analyser DIANA are presented. Recent high precision experiments require, on the side of the theory, high-precision calculations resulting in the evaluation of higher loop diagrams in the Standard Model. For specific processes thousands of multiloop Feynman diagrams do contribute. Of course, the contribution...