Can I apply polyurethane to my hardwood floors in sections?
Surface finishes are notoriously difficult to get smooth when the process is interrupted.  The glossier the finish, the harder to have sections blend.

If you are talking about preliminary coats, especially if they will get a light sanding between coats, this is probably ok. For the finish coat, I would strive hard to do it all in one shot.

If you simply cannot, try to find a transition area that will be less noticable, such as an area covered by rugs or furniture.  You also might try cutting the transition from one section/session to another along a long board line, but this is hard with poly.