Showing papers by "Michael Atiyah published in 1977"
TL;DR: In this paper, it was shown that SU(2) Yang-Mills fields in Euclidean 4-space correspond, via the Penrose twistor transform, to algebraic bundles on the complex projective 3-space.
Abstract: Minimum action solutions for SU(2) Yang-Mills fields in Euclidean 4-space correspond, via the Penrose twistor transform, to algebraic bundles on the complex projective 3-space. These bundles in turn correspond to algebraic curves. The implication of these results for the Yang-Mills fields is described. In particular all solutions are rational and can be constructed from a series of AnsatzeA
l
forl≧1.
443 citations
TL;DR: In the representation theory of compact groups, a major role is played by the Peter-Weyl theorem, which asserts that the regular representation L 2(K) decomposes as a countable direct sum of irreducibles with finite multiplicity as mentioned in this paper.
Abstract: In the representation theory of a compact group K, a major role is played by the Peter-Weyl theorem, which asserts that the regular representation L 2(K) decomposes as a countable direct sum of irreducibles with finite multiplicity. For compact connected Lie groups this becomes much more concrete: the irreducibles are explicitly known, their characters are given by the famous Hermann Weyl formula, and there is a uniform geometrical construction for them due to Borel and Weil.
225 citations
TL;DR: It is rigorously shown that the solutions of SU(2) gauge theory depend on 8k - 3 parameters, where k is the Pontrijagin index.
Abstract: A study is made of the self-dual Yang-Mills fields in Euclidean 4-space. For SU(2) gauge theory it is rigorously shown that the solutions depend on 8k - 3 parameters, where k is the Pontrijagin index.
87 citations
2 citations