1. Announcements 10/22 Today: Read 7D – 7F Wednesday: 7.3, 7.5, 7.6 Friday: 7.7, 9, 10, 13 On Web Exam 1 Solutions to Exam 1

2. Questions from the Reading Quiz “The q vector is a little unclear to me. I think I understand how it relates to epsilon, but I'm not sure where it comes from or what values it can have.” Scalar field: Dirac Field: Vector (gauge) field:

3. A simple problem Suppose a photon is heading in along the x 3 axis. Find an interesting way to designate the two polarizations in Coulomb gauge. The boring solution: More interesting: Most interesting:

4. Feynman Rules: External Lines Propagators:The Vertex

5. Announcements 10/24 Today: 7.3, 7.5, 7.6 Friday: 7.7, 9, 10, 13 Monday: Read 8A-8D Laser Tag money is due

6. Pair Creation Calculate the cross-section for e - e +  ff *, where f is a fermion with charge Q

7. Pair Creation (2) To make any particle that isn’t an electron, must have E > 200 m e Let’s also assume m is negligible.

8. Pair Creation (3) Need the dot products

9. Pair Creation (4) Work to the cross-section

10. Electron-Positron Scattering Calculate the cross-section for e - e +  e - e + Relative minus sign Treat electrons as massless Note this diverges at  = 0 Total cross-section is infinity Must be coming from the second diagram

11. Electron-Positron Scattering (2) Expression vanishes in forward direction Could it be due to assuming zero mass? Cross-section is genuinely infinite Large probability of scattering by a very small angle Experimentally, very small angle scattering not measurable

12. Electron-Positron Annihilation Calculate the cross-section for e - e +   Treat electron as massless

13. Electron-Positron Annihilation (2)

14. Electron-Positron Annihilation (3) Identical particles – factor of two Infinite at  = 0 and  Actually, these two angles are the same Infinity is logarithmic and due to approximations Final integral is finite

15. Questions from the Reading Quiz “Why is it that we determine if a Feynman amplitude is gauge invariant by finding that it will equal zero by replacing epsilon- mu with q-mu? I may just be getting lost in the math, but I don't follow where this comes from.”

16. Gauge Invariance The Feynman amplitude must be gauge invariant Recall: we have choice about how to write the EM field for a photon Feynman amplitude should remain unchanged

17. Gauge Invariance (2) The Feynman amplitude must be gauge invariant To check gauge invariance, replace any polarization vector by its corresponding momentum

18. Announcements 10/24 Today: 7.7, 9, 10 Monday: Read 8A-8D Wednesday: Read 8E-8F, 7.10, 7.12 (m e = 0), 7.13 Problem 7.13 uses identity from problem 2.2c

19. Questions from the Reading Quiz “I am a little confused about the loops in QED section. So if loop diagrams contribute extra factors to g, couldn't we add an infinite number of loops to a diagram so that g is always increasing?”

20. Questions from the Reading Quiz “I think what confused me the most was the idea of charged scalars. I'm not sure I understand the purpose seeing as they're not in the standard model. This seems to just be covering all interactions but are they really necessary?”