Neuman-Dirichlet tadpoles as new string states and quantum mechanical particle-wave duality from world-sheet t-duality

摘要

We consider new objects in bosonic open string theory - ND tadpoles, which have N(euman) boundary conditions at one end of the world-sheet and D(irichlet) at the other, must exist due to s - t duality in a string theory with both NN strings and D-branes. We demonstrate how to interpolate between N and D boundary conditions. In the case of mixed boundary conditions the action for a quantum particle is induced on the boundary. Quantum-mechanical particle-wave duality, a dual description of a quantum particle in either the coordinate or the momentum representation, is induced by world-sheet T-duality. The famous (R) over tilde = alpha/R relation is equivalent to the quantization of the phase space area of a Planck cell closed integral pdx = 2 pi (h) over bar. We also introduce a boundary operator Z - a ''Zipper'' which changes the boundary condition from N into D and vice versa. (C) 1997 Elsevier Science B.V.