Consumers and Business Ethics
Prepared for class discussion
By
Prof.S.Suryanarayanan
Consumers as stakeholders (I)
Commonplace argument that businesses are best served by treating their
customers well
So why continued ethical abuses of consumers and poo
Higgs boson decays
24. (a) For a massive spin-one vector boson of four-momentum p , the polarisation vector must satisfy
the constraint
p = 0 .
In the particle rest frame, we have p = (M, 0, 0, 0), and can take the three independent polarisation
4-vector
Higgs boson mass
25. (a) At leading-order, W+ W W+ W scattering is described by four diagrams involving s-channel
and t-channel photon or Z0 exchange,
W+
W+
W+
W+
, Z0
, Z0
W
W
W
W
plus a diagram involving the quartic W gauge coupling,
W+
W+
W
W
plus s-
Pion decay
4. The leading order Feynman diagram for the decay (p1 ) (p3 ) (p4 ) is
d
W
u
The Feynman rules then give the matrix element as
ig
gW 1
gW 1
iMf i = i 2 if p 2
u(p3 ) i 2 (1 5 ) v (p4 )
1
2
q mW
2
2
where the factor u (1 5 )v that would have a
3
SECTION A
1
GAUGE FIELD THEORY
Write brief accounts of two of the following:
(a) particles and antiparticles in quantum eld theory;
[10]
(b) giving non-zero masses to the W and Z bosons but not to the photon;
[10]
(c) giving non-zero masses to three gen
NATURAL SCIENCES TRIPOS
Wednesday 27 April 2011
Part III
14:00 to 15.30
EXPERIMENTAL AND THEORETICAL PHYSICS
Minor Topics: Paper 225 (Gauge Field Theory)
Answer two questions only. The approximate number of marks allotted
to each part of a question is ind
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
MPE 112
Sheet (1st law)
1- system comprising of gas in cylinder at pressure of 689 kPa Fluid expands from a
volume of 0.04 m3 to 0.045 m3 while pressure remains constant. Paddle wheel
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
MPE 112
Sheet (Ideal Gas)
1- Determine the mass of the air in a room whose dimensions are 4 m X 5 m X6 m at 100
kPa and 25C.
2- A pistoncylinder assembly contains 2 lb of air at a tem
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
MPE 112
Sheet (Energy transfer)
1- A gas in a pistoncylinder assembly undergoes an expansion process for which the relationship
between pressure and volume is given by pv n = constant
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
ENGR 360 BLDG
Pre-Junior Students
Sheet (Combustion)
1- State the combustion equation, the corresponding mass balance and find the
A/F ratio for CH4 with air in chemically correct or
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
MPE 112
Sheet (properties)
1-What a can of soft drink at room temperature is put into the refrigerator so
that it will cool. Would you model the can of soft drink as a closed system
o
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
MPE 112
Sheet (properties)
1-What a can of soft drink at room temperature is put into the refrigerator so that it will
cool. Would you model the can of soft drink as a closed system o
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
Revision (Pure Substances)
A rigid tank contains 50 kg of saturated liquid water at 90C. Determine the pressure in the
1- tank and the volume of the tank.
A pistoncylinder device cont
Grand Unication: SU(5)
23. For a ve-component multiplet of fermion elds ,
1
2
= 3 ,
4
5
the gauge-invariant covariant derivative term in the SU(5) Lagrangian is
L = i D ,
(97)
where the covariant derivative is
24
1
A
2aa
D = + ig5
,
a=1
the A (a = 1,
Parameters of the Standard Model
22. (a) Combining
GF
g2
=
8m2
2
W
and
mW =
(96)
vg
2
gives
v2 =
1
,
2 GF
and hence
v=
1
246 GeV .
2 (1.166 105 GeV2 )
The mass of the Higgs boson is given by
m2 = 22 = 2v 2 .
H
The constants and are not predicted by the
Ultraviolet divergences
20. The electron self-energy mass shift m is given to order e2 by
/
d4 k u(p) (p k + m) u(p)
.
4 (k 2 + i) [(p k )2 m2 + i]
(2 )
u(p)u(p) m = ie2
(93)
(a) Averaged over electron spins, the numerator in the integrand above is
1
2
2
Pion decay
4. The leading order Feynman diagram for the decay (p1 ) (p3 ) (p4 ) is
d
W
u
The Feynman rules then give the matrix element as
ig
gW 1
gW 1
iMf i = i 2 if p 2
u(p3 ) i 2 (1 5 ) v (p4 )
1
2
q mW
2
2
where the factor u (1 5 )v that would have a
Compton scattering
5. The two leading-order Feynman diagrams for Compton scattering, (k ) + e (p) (k ) + e (p ),
are
p
k
p
p+k
k
p k
p
k
k
p
The Feynman rules give the matrix elements for the two leading-order diagrams as
(p + k + m)
/
(k ) u (p )
2 m2
Compton scattering
6. When summed over all initial state and nal state electron and photon spin states, the rst diagram
contributes
2
u
4
|M1 | = e
e , spins
e , spins
(p + k + m)
/
u
(p + k )2 m2
u
(p + k + m)
/
u
(p + k )2 m2
,
where the shortha
Quantum Fields
7. The Lagrangian density L for a eld (r , t) is given as
L=
2i
2
t
t
2m
() ( ) V (r ) .
Regard and as the independent variables, rather than Re() and Im() . The Euler-Lagrange
equation for is
L
L
L
=0.
()
t ( /t)
This gives
2
V
The Dirac eld
8. The Dirac Lagrangian density is
LD = i m .
The momentum density conjugate to is then
=
LD
LD
= i 0 = i .
=
(0 )
The Dirac eld operator has the Fourier representation
(r , t) =
cs (k)us (k)eikx + d (k)vs (k)e+ikx ,
s
d3 k N (k)
s
k2 +
The charge operator for a Dirac eld
9. The standard particle spinors us (k) in the Pauli-Dirac representation are
0
1
1
0
,
u 2 (k ) = N
u 1 (k ) = N
(kx iky )/( + m) ,
kz /( + m)
kz /( + m)
(kx + iky )/( + m)
where N = + m. Hence
1
kz
kx iky
0
u (k )u
The Dirac and Majorana Lagrangians
10. The Lagrangian LD for a free Dirac particle is normally written as
LD = i m .
The nal term on the right-hand side is Hermitian,
( ) = ( 0 ) = 0 = ,
but the rst term is not:
( ) = ( 0 ) = ( ) ( ) ( 0 ) = ( ) 0 0 0 = (
Interacting elds: W decay
11. The Lagrangian contribution
g
g
LI = (1 5 ) W (1 5 ) W
22
22
gives the corresponding Hamiltonian interaction terms
g
g
HI = LI = (1 5 ) W + (1 5 ) W .
22
22
(50)
The transition amplitude from rst-order perturbation theory
Interacting scalar elds
12. A Higgs eld self-interaction term
L I = 3
in the Lagrangian gives an interaction term in the Hamiltonian density H = LI of the form
HI = 3 .
The transition amplitude from rst-order perturbation theory is
d4 x f |HI |i = i
S =
Scalar QED
13. The Lagrangian density for a free complex scalar eld (x) is
L0 = ( ) ( ) m2 .
Applying minimal substitution, + iqA , and including a kinetic term 1 F F for the
4
(Hermitian) vector eld A (x) gives the Lagrangian
1
L = F F + ( iqA )( + iqA )