  We use the equations of motion in combination with crossing symmetry to
constrain the properties of interacting fermionic boundary conformal field
theories. This combination is an efficient way of determining operator product
expansion coefficients and anomalous dimensions at the first few orders of the
$\epsilon$ expansion. Two necessary ingredients for this procedure are
knowledge of the boundary and bulk spinor conformal blocks. The bulk spinor
conformal blocks are derived here for the first time. We then consider a number
of examples. For $\phi$ a scalar field and $\psi$ a fermionic field, we study
the effects of a $\phi \bar \psi \psi$ coupling in $4- \epsilon$ dimensions, a
$\phi^2 \bar \psi \psi$ coupling in $3 -\epsilon$ dimensions, and a $(\bar \psi
\psi)^2$ coupling in $2+\epsilon$ dimensions. We are able to compute some new
anomalous dimensions for operators in these theories. Finally, we relate the
anomalous dimension of a surface operator to the behavior of the charge density
near the surface.
