  The calculation of loop amplitudes with parity violation or spin effects
within dimensional regularization needs a consistent definition of gamma5. Also
loop calculations in supersymmetric theories need a consistent definition of
gamma5. In this paper we develop a new formalism, which allows us to define
consistent regularization schemes. We use Grothendieck's K-functor to construct
finite-dimensional vectorspaces of non-integer rank. The rank will play the
role of the ``4-2eps'' in conventional dimensional regularization. We then
define two regularization schemes, one similar to the 't Hooft--Veltman scheme,
the other one as a scheme, where all algebra is performed in four dimensions.
Lorentz invariance is maintained in both cases. However the structure of the
Clifford algebra cannot be preserved. We show that the HV-like scheme and the
four-dimensional scheme correspond to two different deformations of the
Clifford algebra. It is the purpose of this paper to advocate the
four-dimensional scheme for future calculations, since it is easier to use. As
a consistency check we performed explicit one-loop calculations of various
triangle anomalies in both schemes and we found agreement with Bardeen's
results.
