  We introduce a class of regularisable infinite dimensional principal fibre
bundles which includes fibre bundles arising in gauge field theories like
Yang-Mills and string theory and which generalise finite dimensional Riemannian
principal fibre bundles induced by an isometric action. We show that the orbits
of regularisable bundles have well defined, both heat-kernel and zeta function
regularised volumes. We introduce two notions of minimality (which extend the
finite dimensional one) for these orbits, using both heat-kernel and zeta
function regularisation methods and show they coincide. For each of these
notions, we give an infinite dimensional version of Hsiang's theorem which
extends the finite dimensional case, interpreting minimal orbits as orbits with
extremal (regularised) volume.
