Towards an algebraic approach to the discretisation of fermions

Abstract

A discretisation scheme for differential geometry is applied to the problem of constructing lattice actions, the naive and staggered action are thus derived. It is found that after specifying an ansatz for the space of fields, the corresponding lattice action is obtained. The gauging procedure, and the applicability of the method to twisted super-symmetry on a lattice is outlined. Some comments on the QED axial anomaly are made, for the theory in which the lattice projection operator is not inserted.

Comments: 6 pages