Abstract
The geometrical description of spinor fields by E. Kähler is used to formulate a consistent lattice approximation of fermions. The relation to free simple Dirac fields as well as to Susskind's description of lattice fermions is clarified. The first steps towards a quantized interacting theory are given. The correspondence between the calculus of differential forms and concepts of algebraic topology is shown to be a useful method for a completely analogous treatment of the problems in the continuum and on the lattice.
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Becher, P., Joos, H. The Dirac-Kähler equation and fermions on the lattice. Z. Phys. C - Particles and Fields 15, 343–365 (1982). https://doi.org/10.1007/BF01614426
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DOI: https://doi.org/10.1007/BF01614426