Hostname: page-component-5cf477f64f-mgq6s Total loading time: 0 Render date: 2025-04-04T07:28:32.267Z Has data issue: false hasContentIssue false
  • English
  • Français

Polygons and gravitons

Published online by Cambridge University Press:  24 October 2008

N. J. Hitchin
N. J. Hitchin
Affiliation:
Mathematical Institute, Oxford 0X1 3LB
Get access Rights & Permissions [Opens in a new window]

Extract

1. There has been much interest recently in ‘instantons’. These correspond, in differential geometric terms, to connexions in principal bundles over Euclidean 4-space whose curvature satisfies the Yang-Mills equations. The connexion is also required to approach the trivial connexion at infinity. The self-dual solutions have been classified by converting the problem into one of algebraic geometry using the ideas of R. Penrose and R. Ward

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 3 , May 1979 , pp. 465 - 476
Copyright
Copyright © Cambridge Philosophical Society 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Atiyah, M. F., Hitchin, N. J. & Singer, I. M.Self-duality in four-dimensional Riemannian geometry, Proc. R. Soc. Lond. A 362 (1978), 425–461.Google Scholar
(2)Brieskorn-, E.Die Auflösung der rationalen Singularitäten holomorpher Abbildungen. Math. Ann. 178, (1968), 255–270.CrossRefGoogle Scholar
(3)Brieskorn, E.Singular elements of semisimple algebraic groups. In Actes Congres Intern. Math. (1970), t. 2, 279–284.Google Scholar
(4)Eguchi, T. & Hanson, A.Asymptotically flat solutions to Euclidean gravity. Phys. Lett. 74 B (1978), 249–251.CrossRefGoogle Scholar
(5)Gibbons, G. W. & Hawking, S. W.Gravitational multi-instantons, Phys. Lett. B (to appear).Google Scholar
(6)Gibbons, G. W. & Pope, C. N. The positive action conjecture and asymptotically Euclidean metrics in quantum gravity. DAMTP preprint (Cambridge University).Google Scholar
(7)Penrose, R.Nonlinear gravitons and curved twistor theory, Gen. Relativ. Grav. 7, (1976), 31–52.CrossRefGoogle Scholar