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arXiv · hep-lat/9906015

Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories

Takanori Fujiwara·Hiroshi Suzuki·Ke Wu
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Abstract

The axial anomaly in lattice gauge theories has a topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the non-commutative differential calculus~(NCDC) which makes the Leibniz rule of exterior derivatives valid on the lattice. The topological nature of the ``Chern character'' on the lattice becomes manifest in the context of NCDC. Our result provides an algebraic proof of Lüscher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions.

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Takanori Fujiwara, Hiroshi Suzuki, Ke Wu. 1999-11-09. Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories. https://doi.org/10.1016/s0550-3213(99)00706-3

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