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A theoretical model of the transition radiation (TR) emission of an Nelectron bunch must comply with the covariance and the temporal-causalityprinciples. A charge-density-like covariance must indeed imprint the formalexpression of the TR energy spectrum. A causality relation must constrain theemission phases of the radiation pulse to the temporal sequence of the Nelectron collisions onto the metallic screen. Covariance and causality are thetwo faces of the same coin: failing in implementing one of the two constraintsinto the model necessarily implies betraying the other one. The main formalaspects of a covariance and causality consistent formulation of the TR energyspectrum of an N electron beam will be here described with reference to thecase of a radiator surface with an arbitrary size.

Covariance and Causality in the Transition Radiation of an Electron Bunch