  We modify the construction of the spectral triple over an algebra of holonomy
loops by introducing additional parameters in form of families of matrices.
These matrices generalize the already constructed Euler-Dirac type operator
over a space of connections. We show that these families of matrices can
naturally be interpreted as parameterizing foliations of 4-manifolds. The
corresponding Euler-Dirac type operators then induce Dirac Hamiltonians
associated to the corresponding foliation, in the previously constructed
semi-classical states.
