Colour sums

The amplitude does not depend on the quark flavour so it is not indicated. (Of course initial and flnal quarks have the same flavour.) 

We shall only deal with the t-channel amplitude. Prom (A2.2.3) in 

We list here some identities, generalized to SU N) where appropriate, which are useful in performing the sums over initial and flnal colour states. The summation convention is assumed throughout this discussion. 

Some further identities, written in both notations, are 

We now illustrate the use of these relations by calculating some colour 

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In the above the colour b is, of course, summed over. Rules for doing colour sums are given in Section A2.5. To calculate the unpolarized cross-section involves forming... 

In fact, each linear polarizability itself consists of a sum of two temis, one potentially resonant and the other anti-resonant, corresponding to die two doorway events, and D, and the window events, and described above. The hyperpolarizability chosen in equation (B1.3.12) happens to belong to the generator. As noted, such tliree-coloiir generators caimot produce Class I spectroscopies (fiill quadrature with tliree colours is not possible). Only the two-colour generators are able to create the Class I Raman spectroscopies and, in any case, only two colours are nomially used for the Class II Raman spectroscopies as well. 

Fig. 8.9. Stress fields at the end of a trench etched in a 15f

Hence, among the direct spanning trees there will be spanning trees of two colours, i.e. their number will be exactly equal to that of the initial substances. There will be one more two-coloured spanning tree formed due to the fact that the reaction sequence includes a reaction that does not involve the participation of the observed substance. A sum of the weights of direct spanning trees can be written as... 

The Phytoplankton Colour (PCI) cumulative sum plot showed a (single) shift (Fig. 5) in the mid 1980s. This was very different from the two shifts in the Phaeocystis plot (mid 1960s and early 1990s, see Fig. 5), which shows again that Phaeocystis does not reflect the variation observed in phytoplankton biomass. Between 1970 and 1985, low phytoplankton abundance (PCI) in the North Sea coincided with a late spring bloom. This... 

If the dashed, bold or coloured lines are not those for an all-suprafacial reaction, as on the right-hand side of Fig. 6.7, for example, all is not lost—simply do the sum to find out whether the drawing corresponds to an allowed reaction or not. The all-suprafacial drawing is no better than the other representations, but it is a quick way to arrive at a drawing showing that a (An + 2) reaction is reasonable and allowed, and it works for a very high proportion of pericyclic reactions. 

To sum up our native fossile Cadmia is our Cobalt, with its several species. But the best manufactured Cadmia is made in furnaces from pyrites, that is marcasite in other words, it is simply made from copper, as Dioscorides teaches. But its name varies with the place where it is manufactured, and with its form and its colour. 

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