Announcements for Physics 624 (Prof. Agashe) - Fall 2010

(1). Take-home final (revised) is here and is due by noon on Wednesday, December 15 in

box outside my office (Rm. 4119).

Please read the guidelines on it (and the questions themselves) very carefully.

Revisions in take-home final are as follows:

In general, you can use mathematica/look up formulae for integrals, although you should

be able to do the ones here "by hand" easily.

Problem 1:

(i) You can simply use Feynman rules given in notes posted at

http://www.physics.umd.edu/courses/Phys624/agashe/F10/notes/scalarQED.pdf

Of course, be careful with signs of momenta and (as usual) think about whether there's be

relative sign between diagrams from exchange of identical final state particles.

(ii) Use xi = 1, i.e., 't Hooft-Feynman gauge, for photon propagator.

(iii) Typo: it should be ( D^mu phi )^dagger in Eq. 1.

(iv). In Eq. 1, phi denotes a complex scalar field of charge -1, whereas in Eq. 3, phi^-

denotes spin-0 particle with charge -1.

(v) Write answer in terms of various momenta (p’s), coupling constant etc. (no need to go

to center-of-mass frame etc.)

Problem 2:

(i) sigma (0 < theta < pi/2) is the differential cross-section integrated over the indicated

theta range (and azimuthal angle integrated over its entire range).

Problem 3:

(i) Typo: cross-section scales like beta^1 (s-wave) or beta^3 (p-wave) just like for decay

width of scalar into fermion-antifermion.

Problem 4:

(i) In part (iv), the idea is to figure out whether anything "goes wrong" if a Yukawa

(ii). Just like in problem 1, use xi = 1, i.e., 't Hooft-Feynman gauge, for photon propagator.

(iii) Typo in Eq, 9: it should be ( D^mu phi )^dagger with D_mu as in Eq. 2.

(iv) Just like in problem 1, in Eq. 9, phi denotes a complex scalar field of charge -1,

whereas in Eq. 10, phi^- denotes spin-0 particle with charge -1.

(v) Just like in problem 1, you can simply use Feynman rules given in notes posted at

http://www.physics.umd.edu/courses/Phys624/agashe/F10/notes/scalarQED.pdf

(2). Please check that all your submitted HW’s have been graded/returned (uncollected HW’s

are in box outside Rm. 4119).

(3). Solutions to all Homeworks have now been posted here.

Earlier announcements:

(4). Rough outline for a few lectures on beyond tree-level: I will probably only have time to

(i) present an outline of the effects of loop/radiative corrections (chapters 11, 12 of

Lahiri and Pal)

(ii) isolate and calculate (as in sections 11.1-11.3 of Lahiri and Pal) the anomalous

magnetic moment part of the vertex correction loop diagram (Fig. 11.1 in Lahiri and Pal)

(More details of renormalization program – as in chapter 12 of Lahiri and Pal - might be

covered in other courses, perhaps in Phys 752)

(5). Homework 9 [revised relative to very 1st version: part 9.7 added and typo in part 9.4 – in

RHS of Eq. 46 -  corrected) and 10 [revised relative to very 1st version: part 10.3.2 (iii)

added] have been assigned here, They are due Wednesday, December 1 and

Wednesday, December 8, respectively.

(6). Notes on scalar QED have been posted here.

(7). Notes on QED cross-section for e+ e- _> mu+ mu- have been posted here.

(8). (Corrected/revised relative to very 1st version: as follows) Homework 8 is also at

above link and is due Monday, November  22:

(i) L and R switched in part 8.3.2 (again, P_e = L, P_mu = R was done in lecture)

(ii) “2 sqrt{2} G_F” (instead of “sqrt{2}…” earlier) in Eq. 39

(iii) Total of 5 sub-parts in part 8.2.1.

(iv) Part 8.2.3 added.

(9). Rough outline for a few lectures starting November 17:

(a). Quantization of EM field:

(i)  I will more or less follow the discussion in Lahiri and Pal, chapter 8, although

in a slightly different order, e.g., I will not discuss the classical Green's function

(section 8.2 and 8.4),but rather discuss directly the propagator after quantizing the

Field.

(ii) Please try to read up section 8.1 before lecture on November 17 - since it is

basically classical EM, I won't go thru' it in much detail in lecture.

(b). QED processes:

(i) I will discuss in lecture the general ideas in sections 9.1-9.3 of Lahiri and Pal.

(ii) I will discuss in lecture only a couple of examples of the specific processes in

sections 9.4-9.8 – most likely electron-positron annihilation into muon-antimuon (section

9.6) in detail and a sketch of process with photon in initial/final state (section 9.7, 9.8).

(10). Notes on fermion-fermion scattering are posted here (a couple of typos on page 4 have

been corrected).

(10). Rough outline of earlier lectures during the week of November 8 and 15:

(a)   Calculation of S-matrix elements, first by "brute force" and then by developing Feynman

rules (along the lines of sections 6.2-6.7 of Lahiri and Pal)…

In particular, I'm most likely
not going to fully work through section 6.2 in lecture (since

it is mostly a "normalization" - and not QFT – issue…

The formulae in this section will, however, will be used later and so I am

(b)  Convert S-matrix elements to physical quantities (finally!) such as decay width and

scattering cross-section, along the lines of chapter 7 of Lahiri and Pal...

In particular,

(i) I'm most likely
not going to fully work through sections 7.1, 7.3 and some parts of

7.4  since it mostly involves figuring out normalization factors (just like section
6.2 above) or is just "kinematics"...

Again, these formulae will be used later...

(ii) I'll work through decay example in
section 7.2.1, but skip section 7.2.2 (and we will

not use the formulae in section 7.2.2 later)...

(iii) I'll work through an example of scattering similar to that in section 7.5