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arXiv · 1906.10930

Landau-Khalatnikov-Fradkin transformation and the mystery of even $\zeta$-values in Euclidean massless correlators

A. V. Kotikov·S. Teber
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Abstract

The Landau-Khalatnikov-Fradkin (LKF) transformation is a powerful and elegant transformation allowing to study the gauge dependence of the propagator of charged particles interacting with gauge fields. With the help of this transformation, we derive a non-perturbative identity between massless propagators in two different gauges. From this identity, we find that the corresponding perturbative series can be exactly expressed in terms of a hatted transcendental basis that eliminates all even Euler $\zeta$-functions. This explains the mystery of even $\zeta$-values observed in multi-loop calculations of Euclidean massless correlators for almost three decades now. Our construction further allows us to derive an exact formula relating hatted and standard $\zeta$-functions to all orders of perturbation theory.

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A. V. Kotikov, S. Teber. 2019-06-26. Landau-Khalatnikov-Fradkin transformation and the mystery of even $\zeta$-values in Euclidean massless correlators. https://doi.org/10.1103/physrevd.100.105017

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