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We present an explicit and exact boost of a relativistic bound state definedat equal time of the constituents in the Born approximation (lowest order inhbar). To this end, we construct the Poincar\'e generators of QED and QCD inD=1+1 dimensions, using Gauss' law to express A^0 in terms of the fermionfields in A^1=0 gauge. We determine the fermion-antifermion bound states in theBorn approximation as eigenstates of the time and space translation generatorsP^0 and P^1. The boost operator is combined with a gauge transformation so asto maintain the gauge condition A^1=0 in the new frame. We verify that theboosted state remains an eigenstate of P^0 and P^1 with appropriatelytransformed eigenvalues and determine the transformation law of the equal-time,relativistic wave function. The shape of the wave function is independent ofthe CM momentum when expressed in terms of a variable, which is quadraticallyrelated to the distance x between the fermions. As a consequence, the Lorentzcontraction of the wave function is proportional to 1/(E-V(x)) and thus dependson x via the linear potential V(x).

Boosting equal time bound states