### 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 language | English |
---|---|

Pages (from-to) | 643-660 |

Number of pages | 18 |

Journal | Nuclear Physics B |

Volume | 569 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Mar 13 2000 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*569*(1-3), 643-660. https://doi.org/10.1016/S0550-3213(99)00706-3

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

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 569, no. 1-3, pp. 643-660. https://doi.org/10.1016/S0550-3213(99)00706-3

}

TY - JOUR

T1 - Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories

AU - Fujiwara, Takanori

AU - Suzuki, Hiroshi

AU - Wu, Ke

PY - 2000/3/13

Y1 - 2000/3/13

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0034642651&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034642651&partnerID=8YFLogxK

U2 - 10.1016/S0550-3213(99)00706-3

DO - 10.1016/S0550-3213(99)00706-3

M3 - Article

AN - SCOPUS:0034642651

VL - 569

SP - 643

EP - 660

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-3

ER -