Classical spectral sum rules and “half-naked” electron effects in radiation from relativistic electrons in external field

Two properties of the radiation emitted by a relativistic electron in an external field, in the classical approximation, are presented in details: 1) spectral sum rules and their relationship with the sum rules for oscillator strengths in atomic physics. Filtered sum rules can be used to remove infrared or ultraviolet divergences. 2) "half-naked electron" effects like the Landau-Pomeranchuk-Migdal and Ternovskij-Shul'ga-Fomin effects. These properties are best understood when introducing the apparent transverse velocity.