Equivariant dimensional regularization

The calculation of loop amplitudes with parity violation or spin effects within dimensional regularization needs a consistent definition of γ5. Also loop calculations in supersymmetric theories need a consistent definition of γ5. 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 rôle of the “4−2ε” in conventional dimensional regularization. We then define two regularization schemes, one similar to the ’t Hooft Veltman scheme, the other one similar to the four-dimensional helicity (FDH) scheme. 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 FDH-like scheme correspond to two different deformations of the Clifford algebra. It is the purpose of this paper to advocate the FDH-like 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. email address : [email protected]