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# PS6 - 253a/Schwartz Due Problem Set 6 1 Consider the...

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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 ξ ). 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 ξ dependence cancels to leading order in ξ for one of the subsets in part i . iii. Show that the ξ dependence in the remaining graphs cancels to leading order in ξ . iv. Show that the whole sum is completely ξ-independent. 2. Compton Scattering ( γe- → γe- ) in scalar QED a) calculate the cross section dσ d Ω for this process as a function of the incoming and...
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PS6 - 253a/Schwartz Due Problem Set 6 1 Consider the...

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