On the Landau-Khalatnikov-Fradkin transformation and the mystery of even zeta-values
Seminar “Quantum field theory”
Date and Time: Wednesday, 4 December 2019, at 11:00 AM
Venue: Blokhintsev Conference Hall, Bogoliubov Laboratory of Theoretical Physics
Seminar topic: «On the Landau-Khalatnikov-Fradkin transformation and the mystery of even zeta-values»
Speaker: A. V. Kotikov
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.