Using six-dimensional quantum electrodynamics (QED6) as an example we
study the one-loop renormalization of the theory both from the six and
four-dimensional points of view. Our main conclusion is that the properly
renormalized four dimensional theory never forgets its higher dimensional
origin. In particular, the coefficients of the neccessary extra counterterms in
the four dimensional theory are determined in a precise way. We check our
results by studying the reduction of QED4 on a two-torus.Comment: LaTeX, 36 pages. A new section added; references improved, typos
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