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.

By using the systematic approach of parent action method, we derive one Weyl-noninvariant and two Weyl-invariant actions of bosonic p-branes (p, 2) starting from the Nambu-Goto action, and establish the duality symmetries in this set of four actions. Moreover, we discover a new bosonic p-brane action (including the string theory) and deduce two corresponding Weyl-invariant formulations by proposing a new special parent action. We find that the same duality symmetries as those mentioned above exist in this new set of actions. The new p-brane actions are also briefly analyzed.

The self-duality of chiral p-forms was originally investigated by Pasti, Sorokin and Tonin in a manifestly Lorentz covariant action with non-polynomial auxiliary fields. The investigation was then extended to other chiral p-form actions. In this paper we point out that the self-duality appears in a wider context of theoretical models that relate to chiral p-forms. We demonstrate this by considering the interacting model of Floreanini-Jackiw chiral bosons and gauge fields, the generalized. chiral Schwinger model GCSM and the latter's gauge invariant formulation, and discover that the self-duality of the GCSM corresponds to the vector and axial vector current duality.

We make hamiltonian analyses of the new set of dual bosonic p-brane (in-cluding string) actions which contain high non-linearity. The di