From Neuman to Dirichlet boundary conditions

Abstract

The Dirichlet boundary conditions for the end‐point of the open string define Dp‐brane. It is parameterized by the rest of coordinates, with Neuman boundary conditions. The relations between background fields can produce the local gauge symmetries of the world‐sheet action. After gauge fixing, some Neuman boundary conditions turn into the Dirichlet ones, decreasing the number of Dp‐brane dimensions. The physical Dp‐brane is gauge invariant part of the initial one. The gauge invariant coordinates are expressed as linear combinations of the effective coordinates and momenta. This fact explains the origin of non‐commutativity and the existence of commutative Dp‐brane coordinates.