  The requirements of conformal invariance for the two point function of the
energy momentum tensor in the neighbourhood of a plane boundary are
investigated, restricting the conformal group to those transformations leaving
the boundary invariant. It is shown that the general solution may contain an
arbitrary function of a single conformally invariant variable $v$, except in
dimension 2. The functional dependence on $v$ is determined for free scalar and
fermion fields in arbitrary dimension $d$ and also to leading order in the
$\vep$ expansion about $d=4$ for the non Gaussian fixed point in $\phi^4$
theory. The two point correlation function of the energy momentum tensor and a
scalar field is also shown to have a unique expression in terms of $v$ and the
overall coefficient is determined by the operator product expansion. The energy
momentum tensor on a general curved manifold is further discussed by
considering variations of the metric. In the presence of a boundary this
procedure naturally defines extra boundary operators. By considering
diffeomorphisms these are related to components of the energy momentum tensor
on the boundary. The implications of Weyl invariance in this framework are also
derived.
