Integrating the lagrangian over spacetime in regular field theory (by regular i mean field theories with noncompact dimensions) gives the action. To do this, one integrates over all spacetime , minus infinity to plus infinity in each dimension. For field theories with compactified dimensions, does one still need to integrate over minus infinity to plus infinity? Or is it necessary to integrate only over the region 0 to 2piR where R is the radius of the compactified dimension? And if anyone can point me to some useful discussions on this, it would be much appreciated.