The Nambu-Goto String: Its Phase-Space Path-Integral

Using the Batalin-Fradkin-Vilkovisky formalism for constrained systems, the space-phase path-integral representation of the free bosonic string propagator is considered and compared with the Polyakov approach. A Gribov problem exists for this system with the consequence that the integration measure over modular space is left undetermined. We initially consider the case of the scalar particle with special emphasis on analogies with the string case. The question of Wick rotations in modular space is also discussed.