  Off-diagonal profiles of local densities (e.g. order parameter or energy
density) are calculated at the bulk critical point, by conformal methods, for
different types of boundary conditions (free, fixed and mixed). Such profiles,
which are defined by a non-vanishing matrix element of the appropriate operator
between the ground state and the corresponding lowest excited state of the
strip Hamiltonian, enter into the expression of two-point correlation functions
on a strip. They are of interest in the finite-size scaling study of bulk and
surface critical behaviour since they allow the elimination of regular
contributions. The conformal profiles, which are obtained through a conformal
transformation of the correlation functions from the half-plane to the strip,
are in agreement with the results of a direct calculation, for the energy
density of the two-dimensional Ising model.
