# Stability and isolation phenomena for Yang-Mills fields

@article{Bourguignon1981StabilityAI,
title={Stability and isolation phenomena for Yang-Mills fields},
author={Jean Pierre Bourguignon and H. Blaine Jr. Lawson},
journal={Communications in Mathematical Physics},
year={1981},
volume={79},
pages={189-230}
}
• Published 1 March 1981
• Mathematics
• Communications in Mathematical Physics
In this article a series of results concerning Yang-Mills fields over the euclidean sphere and other locally homogeneous spaces are proved using differential geometric methods. One of our main results is to prove that any weakly stable Yang-Mills field overS4 with groupG=SU2, SU3 orU2 is either self-dual or anti-self-dual. The analogous statement for SO4-bundles is also proved. The other main series of results concerns gap-phenomena for Yang-Mills fields. As a consequence of the non-linearity…
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## References

SHOWING 1-10 OF 22 REFERENCES
Stability and gap phenomena for Yang-Mills fields.
• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 1979
It is shown that any weakly stable Yang-Mills field of type SU(2) or SU(3) on the four-sphere must be self-dual or anti-self-dual. Any Yang-Mills field on S(n), n >/= 5, is unstable. Examples of
Self-duality in four-dimensional Riemannian geometry
• Mathematics
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
• 1978
We present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis. In particular we apply this to the self-dual
A generalized Morse theory
• Mathematics
• 1964
1. Abstract theory. Let M be a C-Riemannian manifold without boundary modeled on a separable Hubert space (see Lang [3]). For pÇzM we denote by ( , )p the inner product in the tangent space Mp and we
The Theory of Matrices
• L. Mirsky
• Mathematics
The Mathematical Gazette
• 1961
In the last two decades Soviet m athem aticians have produced a series of rem arkable books, whose common feature is the stress laid on thoroughness and intelligibility ra the r than on slickness of
A description of instantons
• Mathematics
• 1978
An explicit description is given for all self-dual Euclidean Yang-Mills fields and their parameter spaces in the theory with unitary gauge group of arbitrary rank.
The theory of matrices
• Mathematics
• 1969