2,210 research outputs found
Operator approach to analytical evaluation of Feynman diagrams
The operator approach to analytical evaluation of multi-loop Feynman diagrams
is proposed. We show that the known analytical methods of evaluation of
massless Feynman integrals, such as the integration by parts method and the
method of "uniqueness" (which is based on the star-triangle relation), can be
drastically simplified by using this operator approach. To demonstrate the
advantages of the operator method of analytical evaluation of multi-loop
Feynman diagrams, we calculate ladder diagrams for the massless theory
(analytical results for these diagrams are expressed in terms of multiple
polylogarithms). It is shown how operator formalism can be applied to
calculation of certain massive Feynman diagrams and investigation of Lipatov
integrable chain model.Comment: 16 pages. To appear in "Physics of Atomic Nuclei" (Proceedings of
SYMPHYS-XII, Yerevan, Armenia, July 03-08, 2006
A (Bounded) Bestiary of Feynman Integral Calabi-Yau Geometries
We define the rigidity of a Feynman integral to be the smallest dimension
over which it is non-polylogarithmic. We argue that massless Feynman integrals
in four dimensions have a rigidity bounded by 2(L-1) at L loops, and we show
that this bound may be saturated for integrals that we call marginal: those
with (L+1)D/2 propagators in (even) D dimensions. We show that marginal Feynman
integrals in D dimensions generically involve Calabi-Yau geometries, and we
give examples of finite four-dimensional Feynman integrals in massless
theory that saturate our predicted bound in rigidity at all loop orders.Comment: 5+2 pages, 11 figures, infinite zoo of Calabi-Yau manifolds. v2
reflects minor changes made for publication. This version is authoritativ
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