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

Abstract

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.

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

References in corpus (4)

• Discretized Yang-Mills and Born-Infeld actions on finite group geometries
• Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravity
• Noncommutative Geometry of Lattice and Staggered Fermions
• Generalized Gauge Theories and Weinberg-Salam Model with Dirac-Kähler Fermions

Cited by in corpus (22)

• Exact Extended Supersymmetry on a Lattice: Twisted N=4 Super Yang-Mills in Three Dimensions
• Twisted Superspace on a Lattice
• Exact Extended Supersymmetry on a Lattice: Twisted N=2 Super Yang-Mills in Two Dimensions
• Noncommutativity Approach to Supersymmetry on the Lattice: SUSY Quantum Mechanics and an Inconsistency
• N=4 Twisted Superspace from Dirac-Kahler Twist and Off-shell SUSY Invariant Actions in Four Dimensions
• Twisted SUSY Invariant Formulation of Chern-Simons Gauge Theory on a Lattice
• Twisted N=2 exact SUSY on the lattice for BF and Wess-Zumino
• Species Doublers as Super Multiplets in Lattice Supersymmetry: Exact Supersymmetry with Interactions for D=1 N=2
• Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
• A discrete model of the Dirac-Kähler equation
• On the Continuum and Lattice Formulations of N=4 D=3 Twisted Super Yang-Mills
• Solutions for the Klein-Gordon and Dirac equations on the lattice based on Chebyshev polynomials
• A conformal group approach to the Dirac-Kähler system on the lattice
• On the chirality of a discrete Dirac-Kähler equation
• The chiral and flavour projection of Dirac-Kahler fermions in the geometric discretization
• On fractional semidiscrete Dirac operators of Lévy-Leblond type
• Lattice calculations on the spectrum of Dirac and Dirac-Kähler operators
• Note on Dirac--Kähler massless fields
• On a correspondence principle between discrete differential forms, graph structure and multi-vector calculus on symmetric lattices
• A discrete Dirac-Kähler equation using a geometric discretisation scheme
• A discrete version of plane wave solutions of the Dirac equation in the Joyce form
• Chiral properties of discrete Joyce and Hestenes equations