2. FDs II and QED Flashcards
What do FDs mathematically represent?
The matrix element for a process going from an initial to a final state
What is scalar QED?
Electrodynamics of spin-0 particles
How do we define the particles in scalar QED?
Φ^(-) for the particle
Φ^(+) for the antiparticle
Φ is the spin 0 field
What are the steps for dealing with the FD in scalar QED to calculate the matrix element M?
- Label verticies
- Slice diagram into fragments
- For each fragment, move against arrows along fermion lines and apply the Feyman rules
- Multiply the maths parts together and simplify
What is the Mandelstan variable S for a scattering process 1 + 2 -> 3 + 4
S = (P1 + P2)^2 = (P3 + P4)^2 = COM Energy^2
What is the Mandelstan variable t for a scattering process 1 + 2 -> 3 + 4
t = (P1 - P3)^2 = (P2 - P4)^2
What is the Mandelstan variable U for a scattering process 1 + 2 -> 3 + 4
U = (P1 - P4)^2 = (P2 - P3)^2
Which type of diagram is the S channel diagram related to?
The propagator of the of a creation diagram
Which type of diagram is the t channel diagram related to?
The standard scattering diagram
Which type of diagram is the U channel diagram related to?
The crossed diagram
What is the coupling factor for the EM force?
α_EM = 1/137
Can pair production happen in a vacuum?
No - Cant conserve E, p, m
Is the QED coupling factor constant?
No - it changes on the 4 momentum of the photon at the vertex
What is a consequence of the QED coupling factor not being a constant?
The electron charge is no longer constant
What is the QED coupling factor a function of for very small distances?
α_EM(-Q^2)
where -Q^2 = q^2 = 4 momentum of the photon
What happens to the structure of the target as we increase -Q^2
More detail should be visible if the target has structure
What happens when you put a charge in a dielectric?
You polarise it locally
- Get polarised dipoles in effect which form a negatively charged “screen” around the positive charge
How does the measured charge on a electron change with distance?
Exponential type decay from q_vac to q_vac / k and tails off at q_vac / k for large r
How is an electron considered classically in a vacuum?
As a point source
How is an electron considered by QFT in a vacuum?
Complicated
- Electron dresses itself in a foam of virtual photons, electrons and positron pairs
- In each loop, the virtual positron is attracted to the parent electron forming a positively charged screen
Wrt electron foam, how does increasing -Q^2 change the measurement of the electric charge?
Increase the resolution of the structure and focus in on the region around the electron
- But it is still an effective charge
Can the true charge of an electron be measured?
No - can’t throw foam away
- Always measure an effective charge
What is -1.602 x10^-19 C equal to?
The effective charge of the electron + the foam at the distance scaled by the -Q^2 of the probe
What value of the charge does the SM predict when -Q^2 -> infinity (wavelength -> 0)
Predicts it goes to infinity
Which regimes does the SM break down?
For very high energy and very small distances
