  Deformations of the canonical spectral triples over the n-dimensional torus
are considered. These deformations have a discrete dimension spectrum
consisting of non-integer values less than n. The differential algebra
corresponding to these spectral triples is studied. No junk forms appear for
non-vanishing deformation parameter. The action of a scalar field in these
spaces is considered, leading to non-trivial extra structure compared to the
integer dimensional cases, which does not involve a loss of covariance.
One-loop contributions are computed leading to finite results for non-vanishing
deformation.
