Future lepton colliders will be precision machines whose physics program includes close study of the Higgs sector and searches for new physics via polarised beams. The luminosity requirements of such machines entail very intense lepton bunches at the interaction point with associated strong electromagnetic fields. These strong fields not only lead to obvious phenomena such as beamstrahlung, but also potentially affect every particle physics process via virtual exchange with the bunch fields. For precision studies, strong field effects have to be understood to the sub-percent level. Strong external field effects can be taken into account exactly via the Furry Picture or, in certain limits, via the Quasi-classical Operator method . Significant theoretical development is in progress and here we outline the current state of play.
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