PS12 - 253a/Schwartz Due Problem Set 12 1(This problem...

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253a/Schwartz Due November 30, 2010 Problem Set 12 1. * (This problem involves path integrals, so I made it a star problem. But it is a rather easy path integral problem, so everyone should be able to do it. The real track two parts are marked **.) Furry’s theorem states that ( 0 | T { A μ 1 ( q 1 ) A μ n ( q n ) }| 0 ) = 0 if n is odd. It is a conse- quence of charge-conjugation invariance. a) In scalar QED, charge conjugation swaps φ and φ . How must A μ transform so that the Lagrangian is invariant? b) Prove Furry’s theorem in scalar QED non-perturbatively using the path integral. c) Does Furry’s theorem hold if the photons are off-shell or just on-shell? d) **Prove Furry’s theorem in QED. e) **In the standard model, charge conjugation is violated by the weak interactions. Does your proof, for correlation functions of photons, still work, or do you expect small violations of Furry’s theorem? 2. Compton scattering, qualitatively. a) Draw all the 1-loop diagrams for Compton scattering in QED.
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