1999/03/17 by Stefan Weinzierl, Weinzierl, Stefan · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Computational Geometry and Mesh Generation #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Topological and Geometric Data Analysis #hep-ph #hep-th #math.QA
paper · pdf · doi:10.48550/arxiv.hep-ph/9903380
Latex, 41 pages
openalex publication_date 1999/03/17 · arxiv created 1999/09/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.