Diagrammatic Tensor Reduction - Jae Goode and Sam Teale

Tensor reduction appears as a step in many QFT calculations, for instance in the reduction of vacuum Feynman integrals for UV counterterm calculation through methods such as the R*-algorithm. The basis of independent vacuum tensors of rank n grows factorially with n and a naive approach to reduction scales in the same way. We present our diagrammatic method for calculating projectors that exploits the symmetry properties of the tensor under index permutation to drastically reduce the size of the system. We discuss our implementation of the method in FORM for tensors with arbitrary numbers of Lorentz indices in the case of 0, 2, and 4 spinor indices. We will discuss complications that arise at increasing numbers of spinor indices and finally implementation into the R*-algorithm and extensions to more general tensor reduction.