# ps5 - Physics 509 Relativistic Quantum Field Theory Problem...

This preview shows pages 1–2. Sign up to view the full content.

Physics 509: Relativistic Quantum Field Theory Problem Set 5 Due Friday, 11 November 2011 20. Coulomb Scattering Peskin, Problem 5.1. Further, under what limit does one recover the result obtained for non-relativistic Coulomb scattering? Show that in this limit, one correctly reproduces the Rutherford formula. 21. Gauge Invariance for Compton Scattering a) Consider QED of a complex scalar φ of mass m and charge e : L = - 1 4 F μν F μν + ( D μ φ * )( D μ φ ) - m 2 φ * φ , where D μ = μ + ieA μ is the covariant derivative. Consider Compton scattering φ ( p 1 ) γ ( k 1 ) φ ( p 2 ) γ ( k 2 ), where the polarization vectors of the photons γ ( k 1 ), γ ( k 2 ) are given by 1 , 2 . Write down the tree level amplitude for this process; there are three diagrams. Gauge invariance in the form of the Ward identity dictates that this amplitude should be invari- ant under the change 1 1 + λk 1 , for any constant λ , and likewise for 2 2 + λk 2 . Check that this is indeed the case; you need only consider the case 1 1 + λk 1 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern