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

@article{Kanamori2004DIRACKHLERFF,
  title={DIRAC–K{\"A}HLER FERMION FROM CLIFFORD PRODUCT WITH NONCOMMUTATIVE DIFFERENTIAL FORM ON A LATTICE},
  author={Issaku Kanamori and Noboru Kawamoto},
  journal={International Journal of Modern Physics A},
  year={2004},
  volume={19},
  pages={695-736}
}
We formulate Dirac–Kahler fermion action by introducing a new Clifford product with noncommutative differential form on a lattice. Hermiticity of the Dirac–Kahler 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–Kahler fermion formulated by the Clifford product. The lattice QCD action with Dirac–Kahler matter fermion is also derived via an inner product defined… 

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References

SHOWING 1-10 OF 118 REFERENCES
N=2 supersymmetric model with Dirac-Kahler fermions from generalized gauge theory in two-dimensions
We investigate the generalized gauge theory which has been proposed previously and show that in two dimensions the instanton gauge fixing of the generalized topological Yang-Mills action leads to a
Generalized Gauge Theories and Weinberg-Salam Model with Dirac-Kaehler Fermions (場の量子論の基礎的諸問題と応用)
We extend the previously proposed generalized gauge theory formulation of the Chern–Simons type and topological Yang–Mills type actions into Yang–Mills type actions. We formulate gauge fields and
Dirac–Kähler Equation
Tensor, matrix, and quaternion formulations of Dirac–Kähler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements
Clifford-like calculus over lattices
We introduce a calculus over a lattice based on a lattice generalization of the Clifford algebras. We show that Clifford algebras, in contrast to the continuum, are not an adequated algebraic
Fermions without spinors
The classical Kähler equation for an inhomogeneous differential form is analysed in some detail with respect to the physical properties of its Minkowski space solutions. Although the components of
Geometrical description of the gauged Dirac-Kähler fields on the lattice.
  • Aratyn, Zimerman
  • Mathematics
    Physical review. D, Particles and fields
  • 1986
We present a geometrical foundation of the lattice gauge theory for Dirac-Kaaumlhler fields in the adjoint representation. We give the homological interpretation of the dual boundary and coboundary
...
1
2
3
4
5
...