Abstract
The chiral anomaly in lattice abelian gauge theory is investigated by applying noncommutative differential geometry (NCDG). A new kind of double complex and descent equation is proposed on an infinite hypercubic lattice in arbitrary even-dimensional Euclidean space in the framework of NCDG. By using the general solutions of descent equation, we derive the chiral anomaly in Abelian lattice gauge theory. The topological origin of the anomaly is nothing but the Chern classes in NCDG.
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Fujiwara, T., Suzuki, H., Wu, K. (2001). Application of Noncommutative Differential Geometry on Lattice to Anomaly Analysis in Abelian Lattice Gauge Theory. In: Maeda, Y., Moriyoshi, H., Omori, H., Sternheimer, D., Tate, T., Watamura, S. (eds) Noncommutative Differential Geometry and Its Applications to Physics. Mathematical Physics Studies, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0704-7_2
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DOI: https://doi.org/10.1007/978-94-010-0704-7_2
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