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

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:

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:

Feynman Rules: External Lines Propagators:The Vertex

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

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

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.

Pair Creation (3) Need the dot products

Pair Creation (4) Work to the cross-section

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

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

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

Electron-Positron Annihilation (2)

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

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.”

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

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

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

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?”

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?”