Boundary conditions as Dirac constraints

In this article we show that boundary conditions call be treated as Lagrang ian and Hamiltonian constraints, Using the Dirac method: we find that bound ary conditions are equivalent tu all infinite chain of second class constra ints. which is a new feature ill the context of constrained systems. Constr ucting the Dirac brackets and the reduced phase space structure for differe nt boundary conditions, we show why mode expanding and then quantizing a fi eld theory with boundary conditions is the proper wag. We also show that il l a quantized field theory subjected to the mixed boundary conditions, the field components are non-commutative.