21 Übersetzungen
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Anwendungsbeispiele Englisch
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- The isomonodromy equations arise as (generic) full dimensional reductions of (generalized) anti-self-dual Yang–Mills equations.
- , that (among other things) relates holomorphic vector bundles on 3-dimensional complex projective space CP3 to solutions of the self-dual Yang–Mills equations on S4.
- The resulting equation is called the Hermite–Einstein equation, and is of special importance in gauge theory, where it appears as a special case of the Yang–Mills equations, which come from quantum field theory, in contrast to the regular Einstein equations which come from general relativity.
- His work on the boundary of the moduli space of solutions to the Yang-Mills equations was used by Simon Donaldson in his proof of Donaldson's theorem.
- Yang-Mills equations (with gauge conditions) are well-determined in definition II, whereas are over-determined in definition I.
- Many examples of noncompact hyperkähler manifolds arise as moduli spaces of solutions to certain gauge theory equations which arise from the dimensional reduction of the anti-self dual Yang–Mills equations: instanton moduli spaces, monopole moduli spaces, spaces of solutions to Nigel Hitchin's self-duality equations on Riemann surfaces, space of solutions to Nahm equations.
- Due to the similarity of the second condition in the Hermitian Yang-Mills equations with the equations for an Einstein metric, solutions of the Hermitian Yang-Mills equations are often called Hermite-Einstein connections, as well as Hermitian Yang-Mills connections.
- They also obtain the equations of an integrable system known as the Euler–Arnold–Manakov top, a generalization of the Euler top, and they state that the Kowalevsaya top is also a reduction of the self-dual Yang-Mills equations.
- He worked in the 1970s on other classical solutions of Yang–Mills equations and conformally invariant quantum field theory.
- Instantons are topologically nontrivial solutions of Yang–Mills equations that absolutely minimize the energy functional within their topological type.
- For example, it is sufficient to ask that a vector bundle have a metric connection; when one does so, one finds that the metric connection satisfies the Yang–Mills equations of motion.
- The Painlevé equations are all reductions of the self dual Yang-Mills equations; see [...].
- Deep study of the Nahm equations was carried out by Nigel Hitchin and Simon Donaldson.
- It is more convenient to classify instantons on a sphere as this is compact, and this is essentially equivalent to classifying instantons on Euclidean space as this is conformally equivalent to a sphere and the equations for instantons are conformally invariant.
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