  Using field-theoretical methods and exploiting conformal invariance, we study
Casimir forces at tricritical points exerted by long-range fluctuations of the
order-parameter field. Special attention is paid to the situation where the
symmetry is broken by the boundary conditions (extraordinary transition).
Besides the parallel-plate configuration, we also discuss the geometries of two
separate spheres and a single sphere near a planar wall, which may serve as a
model for colloidal particles immersed in a fluid. In the concrete case of
ternary mixtures a quantitative comparison with critical Casimir and van der
Waals forces shows that, especially with symmetry-breaking boundaries, the
tricritical Casimir force is considerably stronger than the critical one and
dominates also the competing van der Waals force.
