Homework solution - set # 11 Problem XI.1 :
Give explicitely the muonic part of the GWS Lagrangian for the muon. We can dene :
L =
R = R
L
which is the SU (2)W doublet, singlet respectively.
Lepton sector of the GWS model is then given as :
a
Homework 10
1
11/29/2005
Homework X
Problems:
X.1 Consider the weak decay of the muon + e +e: a. Draw the Feynman diagrams for both the Fermi four-point interaction, and the first-order diagram which has the intermediate weak vector boson. b. C
Homework 9
1
12/14/2005
Homework IX
Problems:
IX.1 Calculate the matrix elements and the cross section for Compton scattering and find the d/d|LAB and tot (the so-called Klein-Nishina cross section; Z. Physik 52 (1927) 853). Hints: See e.g. Griffi
Homework 8
1
11/1/2005
Homework VIII
Problems:
VIII.1 Show that the Lagrangian L = FF leads to the correct equations of motion for the free photon field A. Solution: The Euler-Lagrange equation from this Lagrangian is: 2 A A = 0 . With the Lo
Homework 6
1
11/1/2005
Homework VII
Problems:
VII.1 Scattering of spinless particles: a. Calculate d/d* and the total cross section tot for electromagnetic lowest-order electromagnetic scattering of spin-0 bosons A and B, both with charge +e. b. H
phy557_hw06
PHY557 Homework Set 6
Reading: Homework:
Lecture Notes Due date: Wednesday Oct 19
Hints and Solutions
Problem VI.1 Show that Maxwell's equations are invariant under time reversal. Hints: no hints Solution: Similar to Sect.3.4.1. of th
Homework 5
1
11/1/2005
Homework V and Solutions
V.1. The 0 decay: a. Deduce an expression for the energy of a from the decay 0 in terms of the mass m, the laboratory energy E, and the speed of the 0, and of the emission angle * of the in the
Homework 4
1
11/1/2005
Homework IV and Solutions
Problems:
IV.1 Give arguments based on overall L=0, S=3/2 of the three quarks inside the baryon (lowest-lying state), that the overall symmetry of the combined spin and spatial wave function must b
Homework 3
1
11/1/2005
Homework III and Solutions
Problems:
III.1 Show that the rotation (in spin or isospin space) U() = exp(iI) with I = (I1,I2,I3) = i/2 can be written as: U () = 1 cos( /2) + i sin( /2)
Solution: First, note that:
( )
Homework 2
1
11/1/2005
Homework II and Solutions
Problems:
II.1 Show that: (r) = ( r (r) r ) Solution: Use cylindrical coordinates and the z-axis as the rotation axis for : = z, = z, r = + z z = + +z r z LHS: = z
Homework 1
1
11/1/2005
Homework I and Solutions
Problems:
I.1 Show that 1. e2/(40) = 1.44 MeV fm. 2. =1/137 Solution: 1. e2/(40) = (1.602E19 C)/(4*3.142*8.85E12 F/m) e = 1.440E9 eV m = 1.44 MeV fm 2. e2/(40) / (c) = 1.440 MeV fm / 197.3 MeV fm =