  The investigation of a dilute solution of phantom ideal ring polymers and
ring polymers with excluded volume interactions (EVI) in a good solvent
confined in a slit geometry of two parallel repulsive walls and in a solution
of colloidal particles of big size was performed. Taking into account the
correspondence between the field theoretical $\phi^4$ $O(n)$-vector model in
the limit $n\to 0$ and the behaviour of long-flexible polymers in a good
solvent, the correspondent depletion forces and the forces which exert phantom
ideal ring polymers and ring polymers with EVI on the walls were obtained in
the framework of the massive field theory approach at fixed space dimensions
$d$=3 up to one-loop order. Besides, taking into account the Derjaguin
approximation, the depletion forces between big colloidal particle and a wall
and in the case of two big colloidal particles were calculated. The obtained
results indicate that phantom ideal ring polymers and ring polymers with EVI
due to the complexity of chain topology and for entropical reasons demonstrate
a completely different behaviour in confined geometries compared with linear
polymers.
