Scattering equations: from projective spaces to tropical grassmannians
Scattering equations: from projective spaces to tropical grassmannians
We introduce a natural generalization of the scattering equations, which connect the space of Mandelstam invariants to that of points on ${\mathbb{CP}^1}$, to higher-dimensional projective spaces $\mathbb{CP}^{k-1}$. The standard, $k=2$ Mandelstam invariants, $s_{ab}$, are generalized to completely symmetric tensors $\textsf{s}_{a_1a_2\ldots a_k}$ subject to a `massless' condition $\textsf{s}_{a_1a_2\cdots a_{k-2}\,b\,b}=0$ and to …