Newton potential for DGP brane-world scenario is examined when the extra dimension is semi-infinite. The final form of the potential involves a self-adjoint extension parameter α, which plays a role of an additional mass (or distance) scale. The striking feature of Newton potential in this setup is that the potential behaves as seven-dimensional in long range when α is non-zero. For small α there is an intermediate range where the potential is five-dimensional. Five-dimensional Newton constant decreases with increase of α from zero. In the short range the four-dimensional behavior is recovered. The physical implication of this result is discussed in the context of the accelerating behavior of universe.

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.

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.

A Siegel-type chiral p-form action is proposed in D=2(p+1) spacetime dimensions. The approach we adopt is to realize the symmetric second-rank Lagrange-multiplier field, introduced in Siegel's action, in terms of a normalized multiplication of two (q+1)- form fields with q indices of each field contracted in the even p case, or of two pairs of (q+1)- form fields with q indices of each pair of fields contracted in the odd p case, where the (q+1)- form fields are of external derivatives of one auxiliary q-form field for the former, or of a pair of auxiliary q-form fields for the latter. Using this action, it is straightforward to deduce the recently constructed PST action for q equal to zero. It is found that the Siegel-type chiral p-form action with a fixed p (even or odd) is doubly self-dual in D=2(p+1) spacetime dimensions when the auxiliary field(s) is/are also chosen to be of p-form. This result includes PST's as a special case where only the chiral 0-form action is doubly self-dual in D=2 dimensions.  2001 Elsevier Science B.V. All rights reserved.

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.