Dirac-Kaehler Fermion from Clifford Product with Noncommutative Differential Form on a Lattice

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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1+49 pages, 5 figures. v2: references added, and minor modifications

Scientific paper

10.1142/S0217751X04017628

We formulate Dirac-Kaehler fermion action by introducing a new Clifford product with noncommutative differential form on a lattice. Hermiticity of the Dirac-Kaehler 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-Kaehler fermion formulated by the Clifford product. The lattice QCD action with Dirac-Kaehler matter fermion is also derived via an inner product defined by the Clifford product.

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