A toy model for <i>p</i>-form gauge symmetry

Abstract The abelian ( p + 1)-form gauge field is inherently coupled to the p -brane worldvolume. After quantization, the corresponding p -form gauge transformation is associated with the local phase ambiguity of the p -brane wave functional. In essence, p -form gauge symmetry can be realized as a special construction of generic zero-form gauge symmetry in the functional space of p -brane configurations. The non-abelian generalization is straightforward in the functional space language. To simplify the analysis, we further introduce a toy model where the infinite dimensional functional space of p -brane configurations is replaced by a finite dimensional matrix space. After taking the symmetric trace in the matrix model, the original discussions of the p -form gauge symmetry can be inherited by the toy model.