Fermions on the lattice

Abstract

In our first look at QCD on the lattice in Chap.2 we have already announced that our formulation of lattice fermions has not reached its final form. In particular we still need to take into account the correct statistics. In the first section of this chapter we will show that the required Fermi statistics can be implemented by using anti-commuting numbers for the quark fields, so-called Grassmann numbers. We will discuss the rules for calculating with Grassmann numbers, and we will derive a few key formulas for Gaussian integrals with Grassmann numbers. © 2010 Springer-Verlag Berlin Heidelberg.