Morita Equivalence and Interpolation of The Dirac-Born-infeld Theory on the Non-Commutative Torus

In the noncommutative Dirac-Born-Infeld action with Chern-Simons term, an interpolation field $\mathrm{\Phi }$ is used in both DBI action and Chern-Simons term. The Morita equivalence is discussed in both the lagrangian and the Hamiltonian formalisms, which is more transparent in this treatment.