2. FDs II and QED

Question 1

What do FDs mathematically represent?

Answer 1

The matrix element for a process going from an initial to a final state

Question 2

What is scalar QED?

Answer 2

Electrodynamics of spin-0 particles

Question 3

How do we define the particles in scalar QED?

Answer 3

Φ^(-) for the particle
Φ^(+) for the antiparticle
Φ is the spin 0 field

Question 4

What are the steps for dealing with the FD in scalar QED to calculate the matrix element M?

Answer 4

1. Label verticies
2. Slice diagram into fragments
3. For each fragment, move against arrows along fermion lines and apply the Feyman rules
4. Multiply the maths parts together and simplify

Question 5

What is the Mandelstan variable S for a scattering process 1 + 2 -> 3 + 4

Answer 5

S = (P1 + P2)^2 = (P3 + P4)^2 = COM Energy^2

Question 6

What is the Mandelstan variable t for a scattering process 1 + 2 -> 3 + 4

Answer 6

t = (P1 - P3)^2 = (P2 - P4)^2

Question 7

What is the Mandelstan variable U for a scattering process 1 + 2 -> 3 + 4

Answer 7

U = (P1 - P4)^2 = (P2 - P3)^2

Question 8

Which type of diagram is the S channel diagram related to?

Answer 8

The propagator of the of a creation diagram

Question 9

Which type of diagram is the t channel diagram related to?

Answer 9

The standard scattering diagram

Question 10

Which type of diagram is the U channel diagram related to?

Answer 10

The crossed diagram

Question 11

What is the coupling factor for the EM force?

Answer 11

α_EM = 1/137

Question 12

Can pair production happen in a vacuum?

Answer 12

No - Cant conserve E, p, m

Question 13

Is the QED coupling factor constant?

Answer 13

No - it changes on the 4 momentum of the photon at the vertex

Question 14

What is a consequence of the QED coupling factor not being a constant?

Answer 14

The electron charge is no longer constant

Question 15

What is the QED coupling factor a function of for very small distances?

Answer 15

α_EM(-Q^2)

where -Q^2 = q^2 = 4 momentum of the photon

Question 16

What happens to the structure of the target as we increase -Q^2

Answer 16

More detail should be visible if the target has structure

Question 17

What happens when you put a charge in a dielectric?

Answer 17

You polarise it locally

- Get polarised dipoles in effect which form a negatively charged “screen” around the positive charge

Question 18

How does the measured charge on a electron change with distance?

Answer 18

Exponential type decay from q_vac to q_vac / k and tails off at q_vac / k for large r

Question 19

How is an electron considered classically in a vacuum?

Answer 19

As a point source

Question 20

How is an electron considered by QFT in a vacuum?

Answer 20

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

Question 21

Wrt electron foam, how does increasing -Q^2 change the measurement of the electric charge?

Answer 21

Increase the resolution of the structure and focus in on the region around the electron
- But it is still an effective charge

Question 22

Can the true charge of an electron be measured?

Answer 22

No - can’t throw foam away

- Always measure an effective charge

Question 23

What is -1.602 x10^-19 C equal to?

Answer 23

The effective charge of the electron + the foam at the distance scaled by the -Q^2 of the probe

Question 24

What value of the charge does the SM predict when -Q^2 -> infinity (wavelength -> 0)

Answer 24

Predicts it goes to infinity

Question 25

Which regimes does the SM break down?

Answer 25

For very high energy and very small distances