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Pythagoras's theorem on a two-dimensional lattice from a `natural' Dirac operator and Connes's distance formula
Abstract
One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as `natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices.
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Citations
Cites
A no-go theorem for regularizing chiral fermions
Nielsen, H. B., & Ninomiya, M. (1981) · Physics Letters B · doi:10.1016/0370-2693(81)91026-1 · Cited by 951
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Metadata
- Authors
- Dai, J., & Song, X.-C.
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 2001-06-27
- Volume
- 34
- Issue
- 27
- Pages
- 5571-5581
- ISSN
- 0305-4470
- 1361-6447
- Cited by
- 2
- References
- 1
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- The paper
- Dai, J., & Song, X.-C. (2001). Pythagoras's theorem on a two-dimensional lattice from a `natural' Dirac operator and Connes's distance formula. Journal of Physics A: Mathematical and General. https://doi.org/10.1088/0305-4470/34/27/307
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