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

Takanori Fujiwara, Hiroshi Suzuki, Ke Wu

Research output: Contribution to journalArticle

36 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)643-660
Number of pages18
JournalNuclear Physics B
Volume569
Issue number1-3
DOIs
Publication statusPublished - Mar 13 2000
Externally publishedYes

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differential calculus
gauge theory
anomalies
theorems
operators

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

Cite this

Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories. / Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke.

In: Nuclear Physics B, Vol. 569, No. 1-3, 13.03.2000, p. 643-660.

Research output: Contribution to journalArticle

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