Bibliography
From Islands
This page contains a (by no means exhaustive) list of references of relevance for the Nahm equations. The original papers of Werner Nahm are also available.
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Papers and reviews
| Title | Author | Reference | Source | Comments |
|---|---|---|---|---|
| Construction of instantons | M.F. Atiyah, N. J. Hitchin, V.G. Drinfeld, Yu.I. Manin | Phys. Lett. A65:185-187,1978. | ||
| Nahm’s transformation for instantons | Peter J. Braam, Pierre van Baal | Comm. Math. Phys. Volume 122, Number 2 (1989), 267-280 | http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1104178397 | |
| Quantised Singularities in the Electromagnetic Field | P.A.M. Dirac | Proc. of the Royal Society of London, 133, No. 821, 60-72 (1931) | ||
| Nahm’s equations and the classification of monopoles | S.K. Donaldson | Comm. Math. Phys. Volume 96, Number 3 (1984), 387-407. | http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103941858 | |
| A description of instantons | V. G. Drinfeld and Yu. I. Manin | Comm. Math. Phys. Volume 63, Number 2 (1978), 177-192 | http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103904525 | |
| Monopoles and Geodesics | N. J. Hitchin | Commun. Math. Phys. 83:579-602,1982. | http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103920970 | |
| On the construction of monopoles | N. J. Hitchin | Commun. Math. Phys. 89:145-190,1983. | http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103922679 | |
| Monopoles, Minimal Surfaces and Algebraic Curves | N. J. Hitchin | Sem. de Math. Sup. 105. Les Presses de l'Univ, de Montreal (1987) | ||
| Symmetric Monopoles | N. J. Hitchin, N. S. Manton, M. K. Murray | Nonlinearity, Volume 8, Number 5, 1995 pp. 661-692 | http://arxiv.org/pdf/dg-ga/9503016 | |
| Magnetic Monopoles in Unified Gauge Theories | G. 't Hooft | Nuclear Physics B 79, 276-284 (1974) | ||
| On the Construction of Monopoles for the Classical Groups | J. Hurtubise, M. K. Murray | Commun. Math. Phys. 122, 35-89 (1989) | http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1104178316 | |
| Multimonopoles | C. Houghton | Cambridge University, Doctoral Thesis (1997) | http://www.maths.tcd.ie/~houghton/PAPERS/Thesis.pdf | |
| A survey on Nahm transform | M. Jardim | J Geom Phys 52 (2004) 313-327 | http://arxiv.org/abs/math?papernum=0309305 | |
| SU(2) calorons and magnetic monopoles | K Lee, C Lu | Phys. Rev. D 58, 025011 (1998) | http://prola.aps.org/pdf/PRD/v58/i2/e025011 | |
| Particle Spectrum in Quantum Field Theory | A.M. Polyakov | JETP Lett. 20, 194 (1974) | ||
| Exact Classical Solution for the 't Hooft Monopole and the Julia-Zee Dyon | M.K. Prasad, C.M. Sommerfield | Phys. Rev. Lett. \textbf{35}, 760-762 (1975) | ||
| Instantons and monopoles in Yang-Mills gauge field theories | M. K Prasad | Physica 167-191 (1980) | ||
| On a generalized Fourier transform of instantons over flat tori | H. Schenk | Comm. Math. Phys. Volume 116, Number 2 (1988), 177-183. | http://projecteuclid.org/handle/euclid.cmp/1104161298 | |
| Magnetic Monopole Dynamics, Supersymmetry, and Duality | E. J. Weinberg, P. Yi | arXiv:hep-th/0609055v2 | http://arxiv.org/abs/hep-th/0609055 | 253 page review |
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Other material
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Books (introductory and background)
- V.I. Arnold, Mathematical Methods of Classical Mechanics, Springer
- B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, R. G. Burns, Modern Geometry-Methods and Applications, Springer
- L. Landau, E. Lifshitz, Mechanics, Butterworth Heineman
- L. Landau, E. Lifshitz, The Classical Theory of Fields, Butterworth Heineman
- C. Nash and S .Sen, Topology and Geometry for Physicists, 1st Edition, Academic Press (1983)
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Books (advanced)
- M.F. Atiyah, N.J. Hitchin, The Geometry and Dynamics of Magnetic Monopoles, Princeton University Press, Princeton, 1988.
- S. K. Donaldson, P. B. Kronheimer, The Geometry of Four-Manifolds, Oxford University Press
- L.J. Mason, N.M.J Woodhouse, Integrability, Self-duality, and Twistor Theory, Oxford University Press
- N. Manton, P. Sutcliffe, Topological Solitons, Cambridge University Press
- Y. Shnir, Magnetic Monopoles, Springer
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Online material
- Notes on gauge theory and electromagnetic duality by José Figueroa-O'Farrill.
- TASI lectures on solitons by David Tong.
