p-Branes Electric-Magnetic Duality and Stueckelberg/Higgs Mechanism

We study the vacuum functional for a system of p-branes interacting with Maxwell fields of higher rank. This system represents a generalization of the usual electrodynamics of point particles, with one essential difference: the 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 twofold. First, we wish to exploit the breaking of gauge invariance due to the presence of a physical boundary in order to generate mass as an alternative to the Higgs mechanism. Second, we wish to investigate how the new mechanism of mass generation is affected by the duality transformation between electric 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-integral formulation is that it enables us to Fourier transform the field strength (rather than the gauge potential) directly. To our knowledge, this field strength formulation represents a new application of the path-integral method, and it leads, in a straightforward way, to the dual representation of the vacuum functional. We find that the effect of the dual transformation is essentially that of exchanging the roles of the gauge fields defined respectively on the “bulk” and “boundary" of the p-brane history.