DIRAC–KÄHLER FERMION FROM CLIFFORD PRODUCT WITH NONCOMMUTATIVE DIFFERENTIAL FORM ON A LATTICE

Abstract

We formulate Dirac–Kähler fermion action by introducing a new Clifford product with noncommutative differential form on a lattice. Hermiticity of the Dirac–Kähler action requires to choose the lattice structure having both orientabilities on a link. The Kogut–Susskind fermion and the staggered fermion actions are derived directly from the Dirac–Kähler fermion formulated by the Clifford product. The lattice QCD action with Dirac–Kähler matter fermion is also derived via an inner product defined by the Clifford product.