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- In physics and mathematics, and especially differential geometry and gauge theory, the Yang–Mills equations are a system of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations of the Yang–Mills action functional. They have also found significant use in mathematics. Solutions of the equations are called Yang–Mills connections or instantons. The moduli space of instantons was used by Simon Donaldson to prove Donaldson's theorem. (en)
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- The dx1⊗σ3 coefficient of a BPST instanton on the '-slice of R4 where σ3 is the third Pauli matrix . The dx2⊗σ3 coefficient . These coefficients determine the restriction of the BPST instanton A with g=2,ρ=1,z=0 to this slice. The corresponding field strength centered around z=0 . A visual representation of the field strength of a BPST instanton with center z on the compactification S4 of R4 . The BPST instanton is a solution to the anti-self duality equations, and therefore of the Yang–Mills equations, on R'4. This solution can be extended by Uhlenbeck's removable singularity theorem to a topologically non-trivial ASD connection on S4''. (en)
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- -y- plot; BPST instanton.png (en)
- BPST on sphere.png (en)
- Curvature of BPST Instanton.png (en)
- X- plot; BPST instanton.png (en)
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- In physics and mathematics, and especially differential geometry and gauge theory, the Yang–Mills equations are a system of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations of the Yang–Mills action functional. They have also found significant use in mathematics. Solutions of the equations are called Yang–Mills connections or instantons. The moduli space of instantons was used by Simon Donaldson to prove Donaldson's theorem. (en)
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- Yang–Mills equations (en)
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_plot;_BPST_instanton.png?width=300)
_plot;_BPST_instanton.png){kind=link}
_plot;_BPST_instanton.png){kind=link}