Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 306 / 3 / b

Table of contents
- Solution b

Solution

Write the position-dependent factor as

e^{f}

, with

f = α^{'} \sum_{j < l} p_{j} \cdot p_{l} lo g ∣ z_{j} - z_{l} ∣.

In the fixed-angle hard-scattering limit the integral is governed by stationary points. Differentiation gives the scattering equations

j \neq = i \sum \frac{p _{i} \cdot p _{j}}{z _{i} - z _{j}} = 0, j \neq = i \sum \frac{p _{i} \cdot p _{j}}{z ˉ _{i} - z ˉ _{j}} = 0 .

Only

m - 3

complex equations are independent after quotienting by

S L (2, C)

.

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