The Structure of the Bern-Kosower Integrand for the N-Gluon Amplitude

An ambiguity inherent in the partial integration procedure leading to the Bern-Kosower rules is fixed in a way which preserves the complete permutation symmetry in the scattering states. This leads to a canonical version of the Bern-Kosower representation for the one-loop N - photon/gluon amplitudes, and to a natural decomposition of those amplitudes into permutation symmetric gauge invariant partial amplitudes. This decomposition exhibits a simple recursive structure.Comment: 12 pages, no figures, latex, uses dina4.st

QED in the worldline representation

Simultaneously with inventing the modern relativistic formalism of quantum electrodynamics, Feynman presented also a first-quantized representation of QED in terms of worldline path integrals. Although this alternative formulation has been studied over the years by many authors, only during the last fifteen years it has acquired some popularity as a computational tool. I will shortly review here three very different techniques which have been developed during the last few years for the evaluation of worldline path integrals, namely (i) the ``string-inspired formalism'', based on the use of worldline Green functions, (ii) the numerical ``worldline Monte Carlo formalism'', and (iii) the semiclassical ``worldline instanton'' approach.Comment: 18 pages, 7 figures, talk given at VI Latinamerican Symposium on High Energy Physics, Nov. 1-8, 2006, Puerto Vallarta, Mexico; references added and corrected (no other changes

One loop photon-graviton mixing in an electromagnetic field: Part 1

Photon-graviton mixing in an electromagnetic field is a process of potential interest for cosmology and astrophysics. At the tree level it has been studied by many authors. We consider the one-loop contribution to this amplitude involving a charged spin 0 or spin 1/2 particle in the loop and an arbitrary constant field. In the first part of this article, the worldline formalism is used to obtain a compact two-parameter integral representation for this amplitude, valid for arbitrary photon energies and background field strengths. The calculation is manifestly covariant througout.Comment: 27 pages, final published version (minor corrections

A Quantum Field Theoretical Representation of Euler-Zagier Sums

We establish a novel representation of arbitrary Euler-Zagier sums in terms of weighted vacuum graphs. This representation uses a toy quantum field theory with infinitely many propagators and interaction vertices. The propagators involve Bernoulli polynomials and Clausen functions to arbitrary orders. The Feynman integrals of this model can be decomposed in terms of an algebra of elementary vertex integrals whose structure we investigate. We derive a large class of relations between multiple zeta values, of arbitrary lengths and weights, using only a certain set of graphical manipulations on Feynman diagrams. Further uses and possible generalizations of the model are pointed out.Comment: Standard latex, 31 pages, 13 figures, final published versio

A covariant representation of the Ball-Chiu vertex

In nonabelian gauge theory the three-gluon vertex function contains important structural information, in particular on infrared divergences, and is also an essential ingredient in the Schwinger-Dyson equations. Much effort has gone into analyzing its general structure, and at the one-loop level also a number of explicit computations have been done, using various approaches. Here we use the string-inspired formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation in all cases. The vertex is computed fully off-shell and in dimensionally continued form, so that it can be used as a building block for higher-loop calculations. We find that the Bern-Kosower loop replacement rules, originally derived for the on-shell case, hold off-shell as well. We explain the relation of the structure of this representation to the low-energy effective action, and establish the precise connection with the standard Ball-Chiu decomposition of the vertex. This allows us also to predict that the vanishing of the completely antisymmetric coefficient function S of this decomposition is not a one-loop accident, but persists at higher loop orders. The sum rule found by Binger and Brodsky, which leads to the vanishing of the one-loop vertex in N=4 SYM theory, in the present approach relates to worldline supersymmetry.Comment: 32 pages, 1 figure, final revised version (calculation of the two-point functions included, minor corrections, references added