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The Yang-Mills equations over Riemann surfaces
Abstract
The Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory. The main result is that this is a ‘perfect' functional provided due account is taken of its gauge symmetry. This enables topological conclusions to be drawn about the critical sets and leads eventually to information about the moduli space of algebraic bundles over the Riemann surface. This in turn depends on the interplay between the holomorphic and unitary structures, which is analysed in detail.
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Citations
Cites
Principles of Algebraic Geometry
Griffiths, P., & Harris, J. (1994) · Wiley · doi:10.1002/9781118032527 · Cited by 6,765
Mumford, D., Fogarty, J., & Kirwan, F. (1994) · Springer Grundlehren · doi:10.1007/978-3-642-57916-5 · Cited by 2,564
Cited by
Quantum field theory and the Jones polynomial
Witten, E. (1989) · Communications in Mathematical Physics · doi:10.1007/bf01217730 · Cited by 4,758
Remarks on the canonical quantization of the Chern-Simons-Witten theory
Elitzur, S., Moore, G., Schwimmer, A., & Seiberg, N. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90436-7 · Cited by 906
The symplectic nature of fundamental groups of surfaces
Goldman, W. M. (1984) · Advances in Mathematics · doi:10.1016/0001-8708(84)90040-9 · Cited by 685
Two dimensional gauge theories revisited
Witten, E. (1992) · Journal of Geometry and Physics · doi:10.1016/0393-0440(92)90034-x · Cited by 651
Geometric quantization of Chern-Simons gauge theory
Axelrod, S., Della Pietra, S., & Witten, E. (1991) · Journal of Differential Geometry · doi:10.4310/jdg/1214446565 · Cited by 350
Metadata
- Authors
- Atiyah, M. F., & Bott, R.
- Venue
- Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- Publisher
- The Royal Society
- Published
- 1983-03-17
- Volume
- 308
- Issue
- 1505
- Pages
- 523-615
- ISSN
- 0080-4614 (ISSN-L)
- 2054-0272
- OpenAlex
- W2078393607
- Cited by
- 1,885
- References
- 2
- FWCI
- 28.36
- Type
- journal article
- Language
- en
- Open access
- closed
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- Atiyah, M. F., & Bott, R. (1983). The Yang-Mills equations over Riemann surfaces. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. https://doi.org/10.1098/rsta.1983.0017
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
