1,880 research outputs found
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
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