Underlying a general noncommutative algebra with both noncommutative co-ordinates and noncommutative momenta in a (1+1)-dimensional spacetime, a chiral boson lagrangian with manifest Lorentz covariance is proposed by linearly imposing a generalized self-duality condition on a noncommutative generalization of massless real scalar fields. A signifi cant property uncovered for noncommutative chiral bosons is that the leftfi and right-moving chiral scalars cannot be distinguished from each other, which originates from the noncommutativity of coordinates and momenta. An interesting result is that Dirac's method can be consistently applied to the constrained system whose lagrangian explicitly contains space and time. The self-duality of the noncommutative chiral boson action does not exist.

The periodic bounce of Born-Infeld theory of D3-branes is derived, and the BPS limit of in nite period is discussed as an example of tachyon condensation. The explicit bounce solution to the Born-Infeld action is interpreted as an unstable fundamental string stretched between the brane and its antibrane.