On the Landau-Khalatnikov-Fradkin transformation and the mystery of even zeta-values
Семинары
Семинар «Теория квантового поля»
Дата и время: среда, 4 декабря 2019 г., в 11:00
Место: Конференц-зал им. Д.И. Блохинцева, Лаборатория теоретической физики им. Н.Н. Боголюбова
Тема семинара: «On the Landau-Khalatnikov-Fradkin transformation and the mystery of even zeta-values»
Докладчик: А. В. Котиков
Аннотация:
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.