The double copy suggests that the basis of the dynamics of general relativity is Yang-Mills theory. Motivated by the importance of the relativistic two-body problem, we study the classical dynamics of colour-charged particle scattering from the perspective of amplitudes, rather than equations of motion. We explain how to compute the change of colour, and the radiation of colour, during a classical collision. We apply our formalism at next-to-leading order for the colour change and at leading order for colour radiation.

Summary 1.Economic forces are recognized as an important driving factor behind current biodiversity losses. This study investigates whether such factors have been important in determining one measure of biodiversity change over the 'long run' -in our case, 400 years -for upland sites in Scotland. 2. A combination of palaeoecological, historical and economic methods is used to construct and then analyse a database of factors contributing to changes in plant diversity over time for 11 upland sites. 3. Using an instrumental variables panel model, we find livestock prices, our proxy for grazing pressure, to be a statistically significant determinant of diversity change, with higher grazing pressures resulting in lower diversity values on average, although site abandonment is also found to result in a fall in plant diversity. Technological change, such as the introduction of new animal breeds, was not found to be a statistically significant determinant. 4. Using later period data (post 1860) on livestock numbers at the parish (local) level, we were able to confirm the main result noted above (3) in terms of the effects of higher grazing pressures on plant diversity. 5. Synthesis and applications . This study shows how data from very different disciplines can be combined to address questions relevant to contemporary conservation and understanding. This novel, interdisciplinary approach provides new insights into the role of economic factors as a driver of biodiversity loss in the uplands. Biodiversity levels have varied considerably over 400 years, partly as a function of land management, suggesting that establishing baselines or 'natural' target levels for biodiversity is likely to be problematic. Changes in livestock grazing pressures brought about by changes in prices had statistically significant effects on estimated plant diversity, as did land abandonment. This suggests that long-term management of upland areas for the conservation of diversity should focus on grazing pressures as a key policy attribute. Another policy implication is that drastic cuts in grazing pressures -such as might occur under current reforms of the Common Agricultural Policy -can have adverse biodiversity consequences.

We study the variance in the measurement of observables during scattering events, as computed using amplitudes. The classical regime, characterised by negligible uncertainty, emerges as a consequence of an infinite set of relationships among multileg, multiloop amplitudes in a momentum-transfer expansion. We discuss two non-trivial examples in detail: the six-point tree and the five-point one-loop amplitudes in scalar QED. We interpret these relationships in terms or a coherent exponentiation of radiative effects in the classical limit which generalises the eikonal formula, and show how to recover the impulse, including radiation reaction, from this generalised eikonal. Finally, we incorporate the physics of spin into our framework.

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1During the course of the nineteenth century the Abbotsford, Bannatyne, Grampian, Maitland, and Spalding Clubs, together with a number of individuals, were responsible for publishing the majority of the documents that related to the Scottish medieval church. 2Although they all devoted a great deal of time and effort in making the papers more accessible in printed form to the general public, the Bannatyne Club undoubtedly made the greatest contribution. Two points differentiate it from its contemporaries and successors. First, the sheer scale of its publishing operation over a relatively short period of time. Second, the importance to successive generations of historians of Scotland of the records of the individual religious houses that it published. These consisted of a series of texts now commonly regarded, and used, as the cartularies of some of the major Scottish religious houses, including Arbroath, Brechin, Dunfermline, Kelso, Melrose, Moray, and Scone.