Hamiltonian formulation of Wilson's lattice gauge theories
Abstract
Wilson's lattice gauge model is presented as a canonical Hamiltonian theory. The structure of the model is reduced to the interactions of an infinite collection of coupled rigid rotators. The gauge-invariant configuration space consists of a collection of strings with quarks at their ends. The strings are lines of non-Abelian electric flux. In the strong-coupling limit the dynamics is best described in terms of these strings. Quark confinement is a result of the inability to break a string without producing a pair.
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Non-Abelian lattice gauge fields have been realized experimentally using cold atoms and electric circuits.
“As of now, non-Abelian lattice gauge fields have been realized experimentally using cold atoms [4,5] and electric circuits [6].”
From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [4]
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“For the gauge part it is the Wilson form (Wilson, 1974), for the fermionic part two choices are Wilson fermions (Wilson, 1974) and staggered or Kogut-Susskind fermions (Kogut and Susskind, 1975; Susskind, 1977).”
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Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions
Cheng, D., Wang, K., Roques-Carmes, C., Lustig, E., Long, O. Y., Wang, H., & Fan, S. (2025) · Nature · doi:10.1038/s41586-024-08259-2 · Cited by 58 · see citing works
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- Authors
- Kogut, J., & Susskind, L.
- Affiliations
- Cornell University (US)
- Tel Aviv University (IL)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1975-01-15
- Volume
- 11
- Issue
- 2
- Pages
- 395-408
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2160049695
- Cited by
- 2,021
- References
- 0
- Citations by year
- 2026: 99 · 2025: 143 · 2024: 115 · 2023: 103 · 2022: 107 · 2021: 98 · 2020: 80 · 2019: 100 · 2018: 48 · 2017: 44 · 2016: 58 · 2015: 47 · 2014: 47 · 2013: 46 · 2012: 34
- FWCI
- 25.03
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › High-Energy Particle Collisions Research
- Keywords
- quark confinement, magnetic flux tubes, strong coupling limit, quark-antiquark pair production
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