A canonical approach to self-duality of Dirichlet 3-brane

The self-duality of Dirichlet 3-brane action under the SL(2, R) duality transformation of type IIB superstring theory is shown in the Hamiltonian form of the path integral for the partition function by performing the direct integration with respect to the boundary gauge field. Through the integration in the phase space the canonical momentum conjugate to the boundary gauge field can be effectively replaced by the dual gauge field.