  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:
namely, that 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 whole analysis is performed by 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 directly, rather than the gauge potential. To our
knowledge, this field strength formulation represents a new application of the
path integral method, and 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 role of the gauge fields
defined respectively on the " bulk'' and "boundary" of the p-brane history.
