We show that non-commutativity in the spacetime coordinates of D-branes, where the end points of the open strings are attached, can be obtained by modifying the canonical Poisson bracket structure, so that it is compatible with the boundary condition. In this approach, the boundary conditions are not treated as constraints. This is similar in spirit to the treatment of Hanson, Regge and Teitelboim, where modified Poison Bracketss were obtained for the free Nambu-Goto string. Those studies were, however, restricted to the case of the bosonic string and membrane only. We extend the same methodology to the interpolating string and superstring both at classical and quantum level. We also consider the problem of noncommutativity using the new normal ordering satisfying boundary conditions. By using the contour argument and the new operator product expansion, we find the commutator among the Fourier components first and then the commutation relations among string's coordinates which reproduces the usual noncommutative structure. We extended our analysis to superstring case also.
Studies on Boundary Conditions and Noncommutativity in String Theory
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