The index theorem of lattice Wilson-Dirac operators via higher index theory. (English) Zbl 1490.19007
In this interesting paper, the author give a proof of the index theorem of lattice Wilson-Dirac operators by using of the index of twisted Dirac operators on the standard torus. The ingredient of the proof is based on the higher index theory of almost flat vector bundles, developed by M. Gromov and H. B. Lawson jun. [Publ. Math., Inst. Hautes Étud. Sci. 58, 83–196 (1983; Zbl 0538.53047)], A. Connes et al. [C. R. Acad. Sci., Paris, Sér. I 310, No. 5, 273–277 (1990; Zbl 0693.53007)] and B. Hanke and T. Schick [J. Differ. Geom. 74, No. 2, 293–320 (2006; Zbl 1122.58011)].
Reviewer: Jianguo Zhang (Shanghai)
MSC:
| 19K56 | Index theory |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 46L80 | \(K\)-theory and operator algebras (including cyclic theory) |
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