  It is shown that the Dirac-Nambu-Goto brane can be described as a point
particle in an infinite dimensional space with a particular metric. This can be
considered as a special case of a general theory in which branes are points in
the brane space ${\cal M}$, whose metric is dynamical, just like in general
relativity. Such a brane theory, amongst others, includes the flat brane space,
whose metric is the infinite dimensional analog of the Minkowski space metric
$\eta_{\mu \nu}$. A brane living in the latter space will be called "flat
brane"; it is like a bunch of non-interacting point particles. Quantization of
the latter system leads to a system of non-interacting quantum fields.
Interactions can be included if we consider a non trivial metric in the space
of fields. Then the effective classical brane is no longer a flat brane. For a
particular choice of the metric in the field space we obtain the
Dirac-Nambu-Goto brane. We also show how a Stueckelberg-like quantum field
arises within the brane space formalism. With the Stueckelberg fields, we avoid
certain well-known intricacies, especially those related to the position
operator that is needed in our construction of effective classical branes from
the systems of quantum fields.
