Stability and isolation phenomena for Yang-Mills fields
Abstract
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 over S 4 with group G=SU2, SU3 or U 2 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 of the Yang-Mills equations, we can give explicit C 0-neighbourhoods of the minimal Yang-Mills fields which contain no other Yang-Mills fields. In this part of the study the nature of the group G does not matter, neither is the dimension of the base manifold constrained to be four.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- March 1981
- DOI:
- 10.1007/BF01942061
- Bibcode:
- 1981CMaPh..79..189B