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Unformatted text preview: 253a/Schwartz Due October 19, 2010 Problem Set 6 1. Consider the following diagram for scalar alchemy, Pb + Pb + Au + + Au : a) what other diagrams contribute at the same order in perturbation theory? b) show explicitly that the sum of the diagrams is gauge invariant (independent of ). Think carefully before you start. This problem can be messy. i. Which subsets of diagrams should cancel on their own? For example, what if the photons were different massless spin 1 fields? Should the cancellation happen at fixed order in the separate charges of the lead or gold atoms? Can you think of any other subsets? ii. Show that the dependence cancels to leading order in for one of the subsets in part i . iii. Show that the dependence in the remaining graphs cancels to leading order in . iv. Show that the whole sum is completely independent. 2. Compton Scattering ( e e ) in scalar QED a) calculate the cross section d d for this process as a function of the incoming and...
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