Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories

Takanori Fujiwara, Hiroshi Suzuki, Ke Wu
2000 Nuclear Physics B  
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
more » ... becomes manifest in the context of NCDC. Our result provides an algebraic proof of L\"uscher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions.
doi:10.1016/s0550-3213(99)00706-3 fatcat:cal2iiwt7ffbfoz6twgwhctrba