Phys 253a
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Problem Set 10 Solutions December 2, 2010
1. (a) The phase space integral for 1 2 is 1 2m d4 q d3 p (2)4 4 (P - p - q) 3 2E (2)3 E (2) p q
This is easiest to evaluate in the center of mass
Phys 253a
1
Problem Set 9 Solutions December 2, 2010 1. (a) There are lots of diagrams. Most of them are just vertex and propagator corrections. The other diagram we'll deal with is the one that's the
253a/Schwartz Due October 26, 2010
Problem Set 7
1. Majorana representation a) Write out the form of the Lorentz generators in the Majorana representation. b) Calculate 5 = i0 1 2 3 in the Majorana re
253a/Schwartz Due September 14, 2010
Problem Set 1
1. Special Relativity Review a) If two protons are approaching each other with 14 TeV center of mass energy, how close are they to the speed of light
253a/Schwartz Due November 30, 2010
Problem Set 12
1. * (This problem involves path integrals, so I made it a star problem. But it is a rather easy path integral problem, so everyone should be able to
253a/Schwartz Due November 16, 2010
Problem Set 10
1. Particle decays. Recall that the decay rate is given by the general formula d = d 3 p2 1 1 |M|2 (2)3 2E2 2E1 d 3 pn 1 (2)4 4(p1 - p2 - (2)3 2En -
Physics 253a
1
Problem Set 4 Solutions October 7, 2010 1. (a) The tree level diagram has a single vertex ig
Recall that the LSZ formula amputates the external legs, so we just have iM = ig. It turns
Phys 253a
1
Problem Set 6 solutions November 7, 2010
1. (a) There are many diagrams one can draw (I count 23 at order e4 ). Many of these are corrections to the two and three point functions for the s
Phys 253a
1
Problem Set 2 Solutions September 30, 2010 1. (a) Remember that dD x has mass dimension -D, while derivatives have mass dimension 1. We'll denote the mass dimension of a field by []. Then
Physics 253a
1
Problem Set 1 Solutions September 21, 2010
cm 1. (a) In the COM frame, one of the protons has energy E2 = m = m(1 - v 2 )- 2 2m2 (where c = 1). Solving for v gives v 1 - with = E 2 . Th
Physics 253a
1
Problem Set 5 Solutions October 26, 2010 1. (a) We need a W ee coupling and a W coupling in order to get a decay of the form e - W- e- An appropriate Lagrangian is L=
f =e,e
1 1 - f (
253a/Schwartz Due November 23, 2010
Problem Set 11
The Higgs is a (hypothetical) real scalar particle which couples to the standard model as 1 1 2 Lhiggs = - ( + m2 ) + iii + i(i - mi + gzZ)i + Z ( +
Physics 253a
1
Problem Set 3 Solutions October 6, 2010
1. (a) In the center of mass frame, the e+ and e- approach each other with opposite cm cm momenta and total energy Ecm : pe+ = E2 (1, 1, 0, 0) an
Phys 253a
1
Problem Set 11 Solutions December 1, 2010
1. (a) On the previous problem set, we calculated the rate for a scalar decay to two particles i i and found = where :=
mh v .
2 mh i (1 - 4x2 )3/
Phys 253a
1
Problem Set 12 Solutions December 4, 2010 1. (a) The kinetic term for is (D ) D = ( - ieA ) ( + ieA ) If we switch and , then clearly we should take A -A to leave the Lagrangian invariant.
253a/Schwartz Due October 5, 2010
Problem Set 4
1. Consider the Lagrangian for 3 theory 1 g L = - ( + m2) + 3 2 3! (1)
a) Draw a tree level feynman diagram for the decay . Write down the corresponding
253a/Schwartz Due October 12, 2010
Problem Set 5
1. Radioactive decay. The muon decays to an electron and two neutrinos through an intermediate massive particle called the W - boson. The muon, electro
253a/Schwartz Due September 21, 2010
Problem Set 2
Problems marked with a * are optional, but strongly recommended. 1. Dimensional analysis. a) A photon coupled to a complex scalar field in D-dimensio
Introduction to Quantum Field Theory
Matthew Schwartz Harvard University
Fall 2009
Table of contents
0 Conventions and Lorentz invariance 0.1 Introduction . . . . . . . . . . 0.2 Conventions . . . . .
UNIVERSITY OF CALIFORNIA, SANTA BARBARA Department of Physics Physics 221A Prof: Joe Polchinski http:/www.kitp.ucsb.edu/~joep/Web221A/221A.html FINAL EXAM Open notes, homework, solutions, Srednicki (t
UNIVERSITY OF CALIFORNIA, SANTA BARBARA Department of Physics Physics 221A Quantum Field Theory Fall 2007
http:/www.kitp.ucsb.edu/~joep/Web221A/221A.html FINAL EXAM SOLUTIONS 1. a) The propagator for
253a/Schwartz Due September 28, 2010
Problem Set 3
Problems marked with a * are optional, but strongly recommended. 1. We found for e+e- + - that the cross section was proportional to 1 + cos2. a) Wor
253a/Schwartz Due October 19, 2010
Problem Set 6
1. Consider the following diagram for scalar alchemy, Pb- + Pb + Au+ + Au -:
a) what other diagrams contribute at the same order in perturbation theory
253a/Schwartz Due November 2, 2010
Problem Set 8
1. Moller scattering is the process e-e- e-e-. Of the tree-level processes in QED in is especially interesting because it involves identical particles.
Phys 253a
1
Problem Set 8 Solutions November 22, 2010
1. (a) The t and u channels both contribute to Moller scattering. In Feynman gauge ( = 1), we have iM = (-ie)2 u3 u1 u4 u2 M = -ig -ig - (-ie)2 u4
253a/Schwartz Due November 9, 2010
Problem Set 9
1. Consider the following diagram for e+e- + - in QED
a) What other diagrams contribute at the same order in perturbation theory? b) Show explicitly th