Once found, these inscrutable rules have helped particle physicists calculate scattering amplitudes at much higher levels of precision than they could achieve with the traditional approach. The restructuring also allowed Dixon and his collaborators to spot the hidden connection between the two seemingly unrelated scattering amplitudes.
Antipode Map
At the heart of the duality is the “antipode map.” In geometry, an antipode map takes a point on a sphere and inverts the coordinates, sending you straight through the sphere’s center to a point on the other side. It’s the mathematical equivalent of digging a hole from Chile to China.
In scattering amplitudes, the antipode map that Dixon found is a bit more
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