Conformal invariance in quantum field theory

With the present trends 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 an idealization