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With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions. That is because conformal field theories form a large class of massless no-scale renormalizable quantum field theories. It is generally believed, however, that renormalization breaks conformal invariance and with the absence of a reported success to find a conformally invariant renormalization scheme, an alternative approach is followed in this thesis. We begin with a conformally invariant theory and study the implications of such idealization. Conformal field theories are populated with new gauge degrees of freedom and the inclusion, in a natural way, of these auxiliary fields may improve the renormalization program. Another remarkable property is the presence of the vacuum mode in the physical subspace of the gauge potential, believed to be associated with spontaneously generated gauge theories called "zero-center modules." In spite of all the work that has been done over the years on conformal field theories, conformal electrodynamics has remained only partially developed. New results...(more)