Mots-clés : Dirac equation
@article{SIGMA_2023_19_a2,
author = {Nigel J. Hitchin},
title = {A {Note} on {Coupled} {Dirac} {Operators}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2023},
volume = {19},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a2/}
}
Nigel J. Hitchin. A Note on Coupled Dirac Operators. Symmetry, integrability and geometry: methods and applications, Tome 19 (2023). http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a2/
[1] Atiyah M.F., “Complex fibre bundles and ruled surfaces”, Proc. London Math. Soc., 5 (1955), 407–434 | DOI
[2] Atiyah M.F., Hitchin N.J., Singer I.M., “Self-duality in four-dimensional Riemannian geometry”, Proc. Roy. Soc. London Ser. A, 362 (1978), 425–461 | DOI
[3] Atiyah M.F., Singer I.M., “The index of elliptic operators. V”, Ann. of Math., 93 (1971), 139–149 | DOI
[4] Beauville A., Narasimhan M.S., Ramanan S., “Spectral curves and the generalised theta divisor”, J. Reine Angew. Math., 398 (1989), 169–179 | DOI
[5] Bourguignon J.-P., “L'opérateur de Dirac et la géométrie riemannienne”, Rend. Sem. Mat. Univ. Politec. Torino, 44, 1986, 317–359
[6] Bourguignon J.-P., Gauduchon P., “Spineurs, opérateurs de Dirac et variations de métriques”, Comm. Math. Phys., 144 (1992), 581–599 | DOI
[7] Bourguignon J.-P., Hijazi O., Milhorat J.L., Moroianu A., Moroianu S., A spinorial approach to Riemannian and conformal geometry, EMS Monogr. Math., Eur. Math. Soc. (EMS), Zürich, 2015 | DOI
[8] Bourguignon J.-P., Lawson H.B., “Stability and isolation phenomena for Yang–Mills fields”, Comm. Math. Phys., 79 (1981), 189–230 | DOI
[9] Bourguignon J.-P., Lawson H.B., Simons J., “Stability and gap phenomena for Yang–Mills fields”, Proc. Nat. Acad. Sci. USA, 76 (1979), 1550–1553 | DOI
[10] Gaiotto D., “S-duality and boundary conditions and the geometric Langlands program”, String-Math 2016, Proc. Sympos. Pure Math., 98, Amer. Math. Soc., Providence, RI, 2018, 139–179, arXiv: 1609.09030 | DOI
[11] Gawȩdzki K., Tran-Ngoc-Bich P., “Self-duality of the ${\rm SL}_2$ Hitchin integrable system at genus $2$”, Comm. Math. Phys., 196 (1998), 641–670, arXiv: solv-int/9710025 | DOI
[12] Hitchin N.J., “Linear field equations on self-dual spaces”, Proc. Roy. Soc. London Ser. A, 370 (1980), 173–191 | DOI
[13] Hitchin N.J., “Spinors, Lagrangians and rank 2 Higgs bundles”, Proc. Lond. Math. Soc., 115 (2017), 33–54, arXiv: 1605.06385 | DOI
[14] Narasimhan M.S., Ramanan S., “Moduli of vector bundles on a compact Riemann surface”, Ann. of Math., 89 (1969), 14–51 | DOI
[15] Oxbury W., Stable bundles and branched coverings over Riemann surfaces, Ph.D. Thesis, University of Oxford, 1987
[16] Sadun L., Segert J., “Non-self-dual Yang–Mills connections with nonzero Chern number”, Bull. Amer. Math. Soc. (N.S.), 24 (1991), 163–170 | DOI
[17] Sibner L.M., Sibner R.J., Uhlenbeck K., “Solutions to Yang–Mills equations that are not self-dual”, Proc. Nat. Acad. Sci. USA, 86 (1989), 8610–8613 | DOI
[18] van Geemen B., Previato E., “On the Hitchin system”, Duke Math. J., 85 (1996), 659–683, arXiv: alg-geom/9410015 | DOI