  The requirements of conformal invariance for two and three point functions
for general dimension $d$ on flat space are investigated. A compact group
theoretic construction of the three point function for arbitrary spin fields is
presented and it is applied to various cases involving conserved vector
operators and the energy momentum tensor. The restrictions arising from the
associated conservation equations are investigated. It is shown that there are,
for general $d$, three linearly independent conformal invariant forms for the
three point function of the energy momentum tensor, although for $d=3$ there
are two and for $d=2$ only one. The form of the three point function is also
demonstrated to simplify considerably when all three points lie on a straight
line. Using this the coefficients of the conformal invariant point functions
are calculated for free scalar and fermion theories in general dimensions and
for abelian vector fields when $d=4$. Ward identities relating three and two
point functions are also discussed. This requires careful analysis of the
singularities in the short distance expansion and the method of differential
regularisation is found convenient. For $d=4$ the coefficients appearing in the
energy momentum tensor three point function are related to the coefficients of
the two possible terms in the trace anomaly for a conformal theory on a curved
space background.
