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 (ps), 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

interaction
is added.

(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 HWs have been graded/returned
(uncollected HWs

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 1^{st} version: part 9.7 added and typo in part 9.4
in

RHS of Eq. 46 - corrected) and 10 [revised
relative to very 1^{st} 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 1^{st} 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 asking
you to

it
read up instead...

(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