In this thesis we obtain the reduced phase space of a massive open string which lives in flat space and interacts with a constant B-field. Using a discretized version of the model, we first obtain the boundary conditions as the equations of motion of the end points. Since the boundary conditions are acceleration free equations of motion, one can treat them as primary Dirac constraints. As the result of consistency conditions the Lagrange multipliers in the total Hamiltonian vanishes; but in contrast to ordinary constrained systems, some new constraints emerge. The consistency of these new constraints gives newer constraints, and the process continues unlimitedly. In this way we find two infinite chains of constraints at the end points of the string. It can be seen directly that all of the constraints are second Dirac brackets . Then the quantization is achieved by changing the Dirac brackets to commutators. We are finally able to calculate the commutators of original fields, by using their expansions in terms of physical modes. The final results show that the coordinate as well as momentum fields are no longer commutating objects. Coordinate and momentum fields have not Poisson brackets in the form of delta function. This means that they are no longer canonical conjugate fields. Keywords : Mixed boundary conditions, Second dir=rtl
