Some Open Problems on Feynman Periods

© 2020, Springer Nature Switzerland AG. Feynman integrals of quantum field theories that contain non-scalar particles go beyond the well-studied leading period associated to primitive Feynman graphs. It is therefore necessary to study the space of periods spanned by all convergent Feynman integrals for a given graph. Even when the leading period is known, this total space of periods is not understood and carries non-trivial structures. After reviewing the leading period, we consider all convergent integrals of a graph and related open questions.