p-branes electric-magnetic duality and Stueckelberg/Higgs mechanism - A path-integral approach

We study the vacuum functional for a system of p-branes interacting with Ma xwell fields of higher rank. This system represents a generalization of the usual electrodynamics of point particles, with one essential difference: t he world-history of a p-brane, due to the spatial extension of the object, may possess a physical boundary. Thus, the objective of this study is twofo ld. First, we wish to exploit the breaking of gauge invariance due to the p resence of a physical boundary in order to generate mass as an alternative to the Higgs mechanism. Second, we wish to investigate how the new mechanis m of mass generation is affected by the duality transformation between elec tric and magnetic branes. The entire analysis is performed using the path-integral method, as opposed to the more conventional canonical approach. The advantage of the path-int egral formulation is that it enables us to Fourier transform the field stre ngth (rather than the gauge potential) directly. To our knowledge, this fie ld strength formulation represents a new application of the path-integral m ethod, and it leads, in a straightforward way, to the dual representation o f the vacuum functional. We find that the effect of the dual transformation is essentially that of exchanging the roles of the gauge fields defined re spectively on the "bulk" and "boundary" of the p-brane history.