  A number of computational results concerning quantum conformal symmetry is
presented. After a review of the connection between conformal symmetry for a
Lagrangian field theory in flat space and Weyl symmetry for the same system
embedded in a gravitational background, which is discussed in chapter 1, in
chapter 2 the 3 energy momentum tensors correlation function is explicitly
computed in three free field theories in 4 dimensions; the result is given for
two of the three operators on the mass-shell. In chapter 3 a general method to
map Green functions built in position space on the ground of symmetry
requirements to momentum space, where they can be computed in terms of Feynman
diagrams, is developed and discussed: an "integrability" condition, allowing to
decide whether a certain correlator can exist within a Lagrangian theory, is
derived. Chapter 4 discusses the possible phenomenological implications of the
conformal anomaly pole which shows up in the 3 point Green function of one
energy momentum tensor with two gauge currents and is interpreted as the
perturbative signature of the pseudo-Goldstone boson of conformal symmetry, the
dilaton. In chapter 5 we present the computation of the completely traced 4
point function of the energy momentum tensor with a method that exploits the
relation between 1-loop counterterms and conformal anomalies, completely
bypassing perturbative computations with Feynman diagrams. Later in chapter 6,
an algorithm is developed which allows to compute recursively the completely
traced Green functions of any number of energy momentum tensors in any
renormalization scheme, starting from the dilaton Wess-Zumino action for
conformal anomalies. This is derived by applying the Weyl-gauging procedure to
the 1-loop counterterms in dimensional regularization. The result is explicitly
derived and tested in 2, 4 and 6 dimensions.
