The dimensionally regularized massless on-shell double box Feynman diagram with powers of propagators equal to one is analytically evaluated for general values of the Mandelstam variables s and t. An explicit result is expressed either in terms of polylogarithms Lia (−t/s), up to a = 4, and generalized polylogarithms Sa,b(−t/s), with a = 1, 2 and b = 2, or in terms of these functions depending ...

There is a universal combinatorial Hopf algebra structure hidden in the process of renormalization [ 1, 2, 3, 4, 5, 6]. The universality of this structure can be conveniently understood if one considers the UV singularities of Feynman graphs from the viewpoint of configuration spaces. Then, the combinatorial structure of renormalization can be summarized as follows. Each Feynman diagram has var...

A topological sigma model based on the pure spinor formalism was recently proposed for the small radius limit of the AdS5 × S 5 superstring. Physical states in this model can be constructed by connecting holes on the worldsheet with Wilson lines of the worldsheet gauge field. The contribution of these states to the topological amplitude is claimed to reproduce the usual Feynman diagram expansio...

It is usually used a complicated combinatorics to prove the Bogoli-ubov — Parasiuk theorem. In the present paper we give a proof of the Bogoliubov — Parasiuk theorem which use a simple combinatorics. To give this proof we interpret Feynman amplitudes as distributions on the space of α-parameters. We will use this technique in the next paper to give a proof that the divergences in nonequilibrium...

We construct and check by explicit Feynman diagram calculations the BRST Ward identities for N = 2 rigid super Yang-Mills theory and N = 2 extended supergravity in four-dimensional Euclidean space without auxiliary fields. We use the Batalin-Vilkovisky formalism. In the supergravity case we need one new contractible pair of complex spinor fields to obtain the usual gauge-fixing term and corresp...

Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic dynamics, as well as the starting semiclassical approximation to the quantum theory. New methods for computing corrections to the semiclassical approximatio...

Different methods for the calculation of cross sections with many QCD particles are compared. To this end, CSW vertex rules, Berends-Giele recursion and Feynman-diagram based techniques are implemented as well as various methods for the treatment of colours and phase space integration. We find that typically there is only a small window of jet multiplicities, where the CSW technique has efficie...

The 4-th order Runge-Kutta method in the complex plane is proposed for numerically advancing the solutions of a system of first order differential equations in one external invariant satisfied by the master integrals related to a Feynman graph. The particular case of the general massive 2-loop sunrise self-mass diagram is analyzed. The method offers a reliable and robust approach to the direct ...

Due to isospin suppression of the otherwise dominant low-energy isovector WeinbergTomosawa πN term in the re-scattering diagram, and the negative interference between the remaining impulse and isoscalar pion re-scattering terms[1], the empirical data for pp → ppπ near threshold is only explained by phenomenological non-pionic, short-range, twobody mechanisms[2], or alternatively by an off-shell...