http://theory.physics.helsinki.fi/~qmii/

Transcription

Quantum Mechanics II
http://theory.physics.helsinki.fi/~qmii/
1
Spring 2009
Lecturer:
Paul Hoyer
C321
Assistant:
Samu Kurki
C304
Lectures:
Mo 12-14
A315
We 12-14
A315
Mo 16-18
A315
Exercises:
191 50681
First lecture on 12 January
Problem solutions should be put in the box on the 2nd floor of the A-wing by Friday at 14.00.
Course description:
Review of basic formalism. Quantum information. Path integrals. Gauge invariance.
The rotation group and angular momentum. Atomic and molecular dynamics.
Parity and time reversal. Density matrix. Field quantization.
Relativistic quantum mechanics and field theory.
Recommended for 3rd year theoretical physics students, 4th-5th year experimental physics students.
The course Quantum mechanics I (or equivalent) is a prerequisite.
Textbooks: J. J. Sakurai: Modern Quantum Mechanics (Addison Wesley 1994) [S]
I. J. R. Aitchison and A. J. G. Hey: Gauge Theories in Particle Physics, Vol. I:
From Relativistic Quantum Mechanics to QED (IOP Publishing, 3rd Edition, 2003) [AH]
J. Niskanen: Kvanttimekaniikka II (Limes 2003) [N]
F. S. Levin: An Introduction to Quantum Theory (Cambridge University Press 2002) [L]
D. J. Griffiths: Introduction to Quantum Mechanics (Prentice Hall) [G]
B. H. Bransden and C. J. Joachain: Quantum Mechanics (Prentice Hall 2000) [BJ]
M. Le Bellac: A Short Introduction to Quantum Information and Quantum Computation (Cambridge Univer
[MB]
Table of Clebsch-Gordan coefficients, spherical harmonics, gradients, Pauli and Dirac matrices.
Quantum Mechanics II in:
1999
2000
2001
2002
2005
2006
2007
2008
Problems of past partial exams: 1/2003
2/2003
1/2004
2/2004
1/2007
2/2007
1/2008
2/2008
Problems of past final exams:
2003
2004
1/2005
2/2005
16.5.2003 4.6.2003
13.8.2003 2.6.2004
16.6.2004 11.8.2004
21.1.2005 8.6.2005
17.8.2005 25.11.2005 30.5.2007 20.6.2007
28.3.2008 28.5.2008
Lecture notes (p. 1-160)
Paul Hoyer Spring 2009
Course
2
description:
Review of basic formalism. Quantum information. Path integrals. Gauge invariance.
The rotation group and angular momentum. Atomic and molecular dynamics.
Parity and time reversal. Density matrix. Field quantization.
Relativistic quantum mechanics and field theory.
Recommended for 3rd year theoretical physics students, 4th-5th year experimental physics students.
The course Quantum mechanics I (or equivalent) is a prerequisite.
T e x t b o o k s : J. J. Sakurai: Modern Quantum Mechanics (Addison Wesley 1994) [S]
I. J. R. Aitchison and A. J. G. Hey: Gauge Theories in Particle Physics, Vol. I:
From Relativistic Quantum Mechanics to QED (IOP Publishing, 3rd Edition, 2003) [AH]
J. Niskanen: Kvanttimekaniikka II (Limes 2003) [N]
F. S. Levin: An Introduction to Quantum Theory (Cambridge University Press 2002) [L]
D. J. Griffiths: Introduction to Quantum Mechanics (Prentice Hall) [G]
B. H. Bransden and C. J. Joachain: Quantum Mechanics (Prentice Hall 2000) [BJ]
M. Le Bellac: A Short Introduction to Quantum Information and Quantum Computation (Camb
[MB]
Table of Clebsch-Gordan coefficients, spherical harmonics, gradients, Pauli and Dirac matrices.
1999
2000
2001
2005
2006
2007
Problems of past partial exams: 1/2003
2/2003
1/2004
1/2007
2/2007
Quantum Mechanics II in:
Problems of past final exams:
2002
2003
2004
2/2004
1/2005
2/2005
16.5.2003 4.6.2003 13.8.2003 2.6.2004
16.6.2004 11.8.200
3
Measurement of the muon magnetic moment
Brookhaven National Lab., E821
http://www.g-2.bnl.gov/
4
gµ/2 = 1.0 011 659 214 (8)(3) e /2mµ
α
=
2π
0.0011614
5
6
Nuclear magnetic resonance imaging: MRI
7
MRI image of knee
Commission prepares to revise MRI directive
Magnetic resonance imaging researchers have welcomed an investigation into the European Commission’s
Physical Agents directive, which they claim would substantially limit the procedures that can be carried out.
A multinational consortium, led by the Finnish Institute of Occupational Health, was chosen by the
Commission on 23 December 2008 to carry out an impact assessment of the legislation. The consortium,
known as FICETTI, will consider five options ranging from not changing the directive to scrapping it
entirely.
http://arxiv.org/abs/0901.3443
8
Solar neutrino detection
Authors: Lino Miramonti
(Submitted on 22 Jan 2009)
Abstract: More than 40 years ago, neutrinos where conceived as a way to test
the validity of the solar models which tell us that stars are powered by nuclear
fusion reactions. The first measurement of the neutrino flux, in 1968 in the
Homestake mine in South Dakota, detected only one third of the expected value,
originating what has been known as the Solar Neutrino Problem. Different
experiments were built in order to understand the origin of this discrepancy. Now
we know that neutrinos undergo oscillation phenomenon changing their nature
traveling from the core of the Sun to our detectors. In the work the 40 year long
saga of the neutrino detection is presented; from the first proposals to test the
solar models to last real time measurements of the low energy part of the neutrino
spectrum.
Comments: 8 pages, 5 figures. III School on Cosmic Rays and Astrophysics August 25 to
September 5, 2008 Arequipa (Peru) AIP conference proceeding
9
10
_
Allowed regions for 2ν oscillations of solar νe (left) and KamLand νe (right).
The different contours correspond to the allowed regions at 90%, 99% and 3σ
CL.
11
Allowed regions from the analysis of atmospheric νµ data (left), K2K (central)
and Minos (right). The different contours correspond to the allowed regions at
90%, 99% and 3σ CL.
12
νe mass limits from decay measurements
http://cupp.oulu.fi/neutrino/nd-mass.html
Physics Today November 2000
Recommended reading for QM II!
http://www.physicstoday.org/pt/vol-53/iss-11/p22.html
13
or: http://theory.physics.helsinki.fi/~qmii/QCrypt_PT.pdf
Recent article on quantum information in Arkhimedes:
http://theory.physics.helsinki.fi/~qmii/Arkhimedes_08-1_mottonen.pdf
14
http://www.magiqtech.com/
A Quantum Leap in Data Encryption
Startup MagiQ Technologies thinks it's got a
sure way to keep data from prying eyes, using
Heisenberg's Uncertainty Principle
More...
Long-Term Security Assurance and
Quantum Key Distribution
Dr. Burt Kaliski, Vice President of Research,
RSA Security & Chief Scientist, RSA
Laboratories
More...
Taking aim at distance, cost of
quantum crypto
Quantum cryptography: when your link has to
be really, really secure
Stay up-to-date with the MagiQ Technologies Newsletter
More...
First Name
A quantum leap for cryptography
GCN.com, DC -
More...
Last Name
Company
Email Address
Fiber optics may beat hackers
UPI
More...
PaulEDN
Hoyer Spring 2009
MagiQ respects your
privacy.
15
http://theory.physics.helsinki.fi/~qmii/Zeilinger_Nature.pdf
Nature June 2007
16
Nielsen and Chuang: Quantum Computation and Quantum Information, p. 532
17
Nielsen and Chuang: Quantum Computation and Quantum Information, p. 532
18
19
http://theory.physics.helsinki.fi/~qmii/Qfactoring_1.pdf
Physics Today, April 2007
http://theory.physics.helsinki.fi/~qmii/Qfactoring_2.pdf
Physics Today, October 2007
Mikko Möttönen: Kvantti-informaatio – tämän vuosisadan vallankumous!?
Arkhimedes 1/08
http://elektra.helsinki.fi/se/a/0004-1920/2008/1/kvanttii.pdf
tai:
http://theory.physics.helsinki.fi/~qmii/Arkhimedes_08-1_mottonen
20
From Sakurai: Modern Quantum Mechanics
21
Physics Today, March 2002, page 20
~qmii/QM+Gravity_PT55(02).pdf
http://arxiv.org/abs/hep-ph/0602093
A quantum mechanical description
of the experiment on the observation of gravitationally bound states
22
Quantum states in the Earth’s gravitational field were observed, when ultra-cold neutrons fall under gravity. The experimental
results can be described by the quantum mechanical scattering model as it is presented here. We also discuss other geometries of the
experimental setup which correspond to the absence or the reversion of gravity. Since our quantum mechanical model describes,
particularly, the experimentally realized situation of reversed gravity quantitatively, we can practically rule out alternative
explanations of the quantum states in terms of pure confinement effects.
Schematic view with mirrors, absorber and quantum
mechanical boundary conditions. In the experiment, one
mirror of length 10 cm or, as an option as shown here, two
bottom mirrors of length 6 cm were used.
Circles: Data from the 2nd run 2002 with one bottom
mirror [16]. Solid: Transmission coefficient from the
phenomenological scattering model. Dash: The
classical expectation for the neutron transmission
coefficient.
23
http://capp.iit.edu/hep/pbar/Phillips-GravityExpt.pdf
24
http://capp.iit.edu/hep/pbar/Phillips-GravityExpt.pdf
2008-12-05
Antimatter gravity
experiment AEGIS
approved at CERN
in December 2008
25
http://www.mpi-hd.mpg.de/kellerbauer/en/
AEGIS experiment approved
The CERN Research Board has approved our proposal for the AEGIS
experiment (Antimatter Experiment: Gravity, Interferometry, Spectroscopy) and
committed itself to an extension of the operation of the Antiproton Decelerator
(AD) facility until 2016. AEGIS will test the gravitational interaction of
antimatter using an antihydrogen beam. The AEGIS proposal had already been
positively evaluated by the scientific committee in January 2008, but the final
go-ahead depended on CERN's continued support for the AD, where AEGIS will
be installed. Construction of the AEGIS apparatus will begin in 2009.
Overview sketch of the AEGIS experiment
http://www.hitachi.com/rd/research/em/abe.html
26
Verification of the Aharonov-Bohm effect
27
http://www.hitachi.com/rd/research/em/abe.html
28
Helsinki University of Technology
SQUID Magnetometers
29
122-SQUID neuromagnetometer
In the middle of 1992, a sophisticated 122channel brain research system became
operational. This instrument is the
culmination of more than ten years of
development of the magnetoencephalographic (MEG) technology in the LTL. The
magnetic field caused by neural currents
flowing in the brain is measured by an array
of 122 superconducting sensors which cover
the subject's head in a helmetlike fashion.
http://ltl.tkk.fi/triennial/squid.html
Paul Hoyer Spring 2009 http://hyperphysics.phy-astr.gsu.edu/HBASE/Solids/Squid.html
• A Personal Witness Account of the Keppe
30
http://arxiv.org/abs/hep-ex/0302011
Motor
• Enviro Energies' magnetically levitated
Mag-Wind
w.magnetmonster.de
e Energy"
You are here: PureEnergySystems.com > News > June 5, 2004
Googling, you also find this:
FE News
es
Specials
Energy Now
Week in FE
etter
t
PureEnergySystems.com > News > June 5, 2004
High Energy Magnetic Monopole
Sequestered by U.S. Government
With resistive forces of at least 10 to 20 tons per square meter at 1/4" thickness, this
material could power a device approximately the size of standard can of oil, delivering
a minimum torque ratio of 1.5 tons of turning force. Witness comes forward after
thirty years despite threats on his life.
Paul Hoyer Spring 2009 by James D. Fauble
Plug
a
31
Physical Review A7 (1973) 1224
Charge of SF6 molecule is less than 2⋅10–19 e
|ep+ee| < 1⋅10–21 ee
32
CLEBSCH-GORDAN
COEFFICIENTS
1
0
+1
1
0
0
+ 1/2 + 1/2 1
+ 1/2 ! 1/2 1/2 1/2 1
! 1/2 + 1/2 1/2 ! 1/2 ! 1
1/2 " 1/2
N ota ti on:
! 1/2 ! 1/2 1
m2
m1
m2
.
.
.
3/2
+ 3/2 3/2 1/2
1 + 1/2 + 1/2
+ 1 + 1/2
1 " 1/2
+ 1 ! 1/2
0 + 1/2
m1
.
.
.
M
M
...
...
Note: A square root should be taken of
each element shown (apart from sign).
2/3 1/3 3/2
1/3 ! 2/3 ! 3/2
! 1 ! 1/2
J
C oefficients
1/3 2/3 3/2 1/2
2/3 ! 1/3 ! 1/2 ! 1/2
0 ! 1/2
! 1 + 1/2
J
1
More complete table of C-G
coefficients, spherical functions etc.
may be found on the QM II home page
!j1 j2 m1 m2 |j1 j2 JM "
= (−1)J−j1 −j2 !j2 j1 m2 m1 |j2 j1 JM "
33
34
8 .0 0
Spin
7 .0 0
P.Desgrolard, M.Giffon, E.Martynov, E.Predazzi, hep-ph/0006244
Regge trajectory
f (2 5 1 0 )
6
2
R e ! (m )
6 .0 0
a 6 (2 4 5 0 )
" 5 (23 5 0)
5 .0 0
f 4 (2 05 0)
a (2 02 0)
4 .0 0
4
" 3(1 70 0 )
# (1 67 0 )
3 .0 0
3
2 .0 0
1 .0 0
0 .0 0
0 .0 0
f 2(1 2 7 0 )
a 2 (1 3 1 8 )
" (77 0 )
#(7 82 )
2 .0 0
4 .0 0
m
2
For unknown
reasons, spins of
elementary
particles are
proportional to
their mass2
6 .0 0
8 .0 0
1 0 .0 0
2
(G eV )
Figure 1: Chew-Frautschi plot for the fully exchange-degen erate f , ω, ρ and a2 trajectories.
The solid line denotes the trajectory with the parameters obtained in our fit; the dashed line
is the trajectory α(m2) = 0.48 + 0.88m2 (m in GeV).
S TANDARD M ODEL H IGGS
35
http://www-cdf.fnal.gov/physics/talks_transp/2008/discrete_08_casal.pdf
t EW symmetry breaking introduced into the SM via the Higgs
mechanism
t Results in massive Higgs boson and mass terms for fermions
t Not yet observed: opportunity for the Tevatron
6
mLimit = 154 GeV
July 2008
Theory uncertainty
Δα(5)
had =
5
0.02758±0.00035
0.02749±0.00012
incl. low Q2 data
Δχ2
4
t LEP direct searches:
3
mH > 114 GeV
2
t Indirect EW constrains:
1
0
mH < 154 GeV
Excluded
30
Preliminary
100
mH [GeV]
Paul Hoyer Spring
Bruno2009
Casal (IFCA)
300
t We exclude at 95% C.L. the production of a SM
Higgs boson of 170 GeV
t First direct exclusion since LEP!
Higgs at Tevatron
DISCRETE08 12/12/2008
6 / 17II
Quantum Mechanics
http://galileo.phys.virginia.edu/classes/751.mf1i.fall02/HydrogenAtom.pdf
Hydrogen atom wave functions
rR(r)
36
l=0
n=3
l=2
r/a0
l=1
http://en.wikipedia.org/wiki/Rydberg_atom
|rR(r)|2 (?)
n=10
l=9
Classical orbits for n = 5:
Rydberg
atoms
En ∝ 1/n2
r n ∝ n2
r/a0
5s (!=0)
l=0
5p (!=1)
|rR(r)|2 (?)
n=10
l=0
5d (!=2)
5f (!=3)
5g (!=4)
l=4
r/a0
37
"#$%&' (&#)$*+#,%&-,&-./0 Atoms
http://www.itkp.uni-bonn.de/~rusetsky/TRENTO06/talks.html
n
4
3
s
p
d
E2p
2
"1s
1
!#
f
C58@2%0(A%D8A25%
3@%6202)6%(E=
()7>878B>)
!$%%%&%%'()%"#$
!%& '()*+,%&-.#/&01(2 )*+,%&-#0.01
}
!1s
E1s
4')%23%25)%6213(7%8(2)109283(%:03(;<1323(
25)%=6%>)?)>%86%658@2)A%0(A%B130A)()A
!"#$%&'()
*+,%%*++Paul
Hoyer Spring
2009
&./0123(
! II
Quantum Mechanics
38
From F. S. Levin: An Introduction to Quantum Theory, p. 706
39
From F. S. Levin, p. 708
40
41
42
43
http://en.wikipedia.org/wiki/Muon-catalyzed_fusion
http://www.triumf.ca/welcome/h-fusion.html
44
Muon Catalysed Fusion
p
Proton
n
Neutron
p n
+
Compound
molecule
n n
p
Tritium
nucleus
Free
muon
n n
p
n n
p
p
n
+
Muonic
tritium nucleus
n n
p p
Alpha
particle
+
n
Free
neutron
Deuterium
nucleus
+
+
Energy
from
fusion
Free
muon
45
This historical review of the discovery of
parity violation may be found at:
http://ccreweb.org/documents/parity/parity.html
46
The positive pion, a spinless particle, initially has zero angular momentum and zero linear momentum (we consider only pion decay at rest). Therefore linear
momentum conservation requires that the decay products (a positive muon and a muon neutrino) are emitted in opposite directions with equal and opposite
momenta; meanwhile, angular momentum conservation requires that they have equal and opposite spin. The weak interaction governing this decay process has the
remarkable property that it creates only ``left-handed'' or ``negative helicity'' neutrinos (i.e. having their spin and angular momentum in opposite directions, as
shown) and ``right-handed'' or ``positive helicity'' antineutrinos, so the µ+ must also have its spin pointing back along its momentum. This gives a beam of perfectly
spin-polarized muons from pion decay - an essential ingredient for µSR.
Γ(π → eνe )
= 1.23 · 10−4
Γ(π → µνµ )
The mirror-image reaction never occurs in nature, because the parity inversion performed by the mirror changes a left-handed neutrino to a right-handed one, which
the weak interaction cannot produce.
http://musr.org/~jess/musr/cap/pidk.htm
http://www.mpi-hd.mpg.de/hfm/CosmicRay/Showers.html
47
Antoine Weis:
www.unifr.ch/physics/frap/3cycle/Lecture2.pdf
48
Atomic physics tests of the Standard Model
THE STANDARD MODEL
· charged currents and neutral currents
THEORY OF PARITY VIOLATION IN ATOMS
· parity violating asymmetry
· parity violating potential and matrix elements
PARITY VIOLATION IN ATOMS: GENERAL CONSIDERATIONS
· allowed and forbidden transitions
· parity violating electric dipole amplitude
· classical representation of PV atom
· q. m. representation of PV atom
· M1 - E1pv interference
· optical rotation experiments
SPECIFIC PARITY VIOLATION EXPERIMENTS IN ATOMS
· optical rotation experiments
· experiments with 133Cs
- field-free circular dichroism
49
www.physics.indiana.edu/~charlie/parity/talks/bouchiat.ps.gz
50
http://en.wikipedia.org/wiki/Electronic_band_structure
Comparison of the electronic band structures
of metals, semiconductors and insulators
http://en.wikipedia.org/wiki/Neutron_electric_dipole_moment51
Transformations of magnetic and electric
dipole moments under parity and time reversal
E P
B →
-E
B
E T
B →
E
-B
A permanent electric dipole moment of a
fundamental particle violates both parity (P) and
time reversal symmetry (T). This is quickly
comprehensible by looking at the neutron with its
magnetic dipole moment and hypothetical electric
dipole moment. Under time reversal, the magnetic
dipole moment changes its direction, whereas the
electric dipole moment stays unchanged. Under
parity, the electric dipole moment changes its
direction but not the magnetic dipole moment. As
the resulting system under P and T is not
symmetric with respect to the initial system, these
symmetries are violated in the case of the
existence of an EDM. Having also CPT
symmetry, the combined symmetry CP is violated
as well.
http://en.wikipedia.org/wiki/Neutron_electric_dipole_moment52
http://www.cambridge.org/resources/052182379X/2064_ch06.pdf
53
Lattice waves
http://en.wikipedia.org/wiki/Phonon
54
Diagonalized
Collection of N+1 independent
harmonic oscillators, labelled by k
For each k, state is labelled by number nk of phonons
55
56
Phonons, photons, pions can be created and annihilated in scattering
_
e+e– → q q g :
γ*
Feynman
diagram
http://www.lnf.infn.it/~levisand/graal/graal_beam_intro.html
57
Backscattered photon beam at ESF (Grenoble):
6 GeV electrons against laser photons
http://www.hep.man.ac.uk/babarph/babarphysics/positron.html
58
This is a picture of one of the first positron tracks observed by
Anderson in 1933. It was taken in a cloud chamber in the
presence of a magnetic field (so the particle paths are curved).
A cloud chamber contains a gas supersaturated with water
vapour. In the presence of a charged particle (such as a
positron), the water vapour condenses into droplets - these
droplets mark out the path of the particle.
The band across the middle is a lead plate, which slows down
the particles. The radius of curvature of the track above the plate
is smaller than that below. This means that the particle is
travelling more slowly above the plate than below it, and hence
it must be travelling upwards. From the direction in which the
path curves one can deduce that the particle is positively
charged. That it is a positron and not a proton can be deduced
from the long range of the upper track - a proton would have
come to rest in a much shorter distance.
Carl Anderson won the 1936 Nobel Prize for Physics for this
discovery.
Picture taken from C.D. Anderson, Physical Review 43, 491
(1933).
http://teachers.web.cern.ch/teachers/archiv/HST2005/bubble_chambers/BCwebsite/index.htm 59
Bubble Chamber
Electrons, positrons and photons
60
The knock-on electron (bottom left) and
the lone Compton electrons show that
negative particles turn to the left.
There are three linked highlighted examples of high energy photons materialising into e+e– pairs in the field
of a nucleus. In the order in which it have happened:
* the first photon materialises (nearest the bottom of the picture);
* the second is most likely a bremsstrahlung photon from the of the first e+e– pair;
* the Compton electron (on the right of the picture) is caused by a bremsstrahlung photon from the e+of the second pair;
* the third e+e– pair (on the left of the picture) is caused by a bremsstrahlung photon from the of the second e+e– pair.
The thick track coming in from the top of the picture (one can tell which way it is going by noticing the
knock-on electron) is a cosmic ray, probably a muon. This is a reminder of the link between cosmology and
particle physics.
http://teachers.web.cern.ch/teachers/archiv/HST2005/bubble_chambers/BCwebsite/index.htm 61
A classic example of a pi mu e decay
π+
+
e+
µ+
This picture was taken in the CERN 2m hydrogen bubble chamber. (We think the incoming beam consists of
K+ particles at 10 GeV/c.)
The little curly electron near the collision point tells us that negative particles turn to the left.
The track that starts going to the right before looping round is a π+. It stops and decays to a µ+ and a muon
neutrino νµ. The muon can only receive about 30 MeV/c (for details click here) in this decay and can only
travel about 1 cm in hydrogen before it , itself, stops. It then decays into a positron (which spirals
characteristically), an electron neutrino νe and a muon-antineutrino .
62
The QED experience
Physical Review 140 (1965) B397
63
In his report to the 12th Solvay Congress (Brussels, 1961) on “The Present Status of Quantum
Electrodynamics” (QED), Feynman called for more insight and physical intuition in QED
calculations. To quote from a particularly relevant passage:
“It seems that very little physical intuition has yet been developed in this subject. In nearly
every case we are reduced to computing exactly a coefficient of some specific term. We have
no way to get a general idea of the result to be expected. To make my view clearer, consider,
for example, the anomalous electron moment, (g–2)/2 = α/2π – 0.328α2/π2 . We have no
physical picture by which we can easily see that the correction is roughly α/2π , in fact, we do
not even know why the sign is positive (other than by computing it). In another field we
would not be content with the calculation of the second order term to three significant figures
without enough understanding to get a rational estimate of the order of magnitude of the third.
We have been computing terms like a blind man exploring a new room, but soon we must
develop some concept of this room as a whole, and to have some idea of what is contained in
it. As a specific challenge, is there any method of computing the anomalous moment of the
electron which, on first rough approximation, gives a fair approximation to the α term and a
crude one to α2 ; and when improved, increases the accuracy of the α2 term, yielding a rough
estimate of α3 and beyond?”
64
Bound states of atoms
U.D. Jentschura et al,
PRL 95 (2005) 163003
65
The accuracy of measurement and theory
66
Many of our most accurate predictions come from QED atoms.
For example, the 2S1/2 – 8S1/2 splitting in Hydrogen:
Δ(2S1/2 – 8S1/2)H = 770 649 350 012.0(8.6) kHz EXP
= 770 649 350 016.1(2.8) kHz QED
U.D. Jentschura et al,
PRL 95 (2005) 163003
The QED result is based on perturbation theory:
– an expansion in α = e2/4π ≈ 1/137.035 999 11(46)
However, the series must diverge since for any α = e2/4π < 0 the electron
charge e is imaginary: The Hamiltonian is not hermitian and probability not
conserved.
F. Dyson
The perturbative expansion is believed to be an asymptotic series.
The good agreement with QED seems fortuituous, from a purely
theoretical point of view.
For a recent discussion of the truncation effects
in asymptotic expansions see Y. Meurice, hep-th/0608097
http://home.fnal.gov/~prebys/talks/rochester_20010926.pdf
67
68
The Nobel Prize in Physics 1980
"for the discovery of violations of fundamental symmetry principles in the decay of
neutral K-mesons"
James Watson Cronin
1/2 of the prize
Val Logsdon Fitch
1/2 of the prize
USA
USA
University of Chicago
Chicago, IL, USA
Princeton University
Princeton, NJ, USA
b. 1931
b. 1923
"for the discovery of the
mechanism of
spontaneous broken
symmetry in subatomic
physics"
"for the discovery of the origin of the broken symmetry
which predicts the existence of at least three families of
quarks in nature"
Photo: Universtity of Chicago
Yoichiro Nambu
1/2 of the prize
b. 1921 (in Tokyo, Japan)
USA
Photo: KEK
Makoto Kobayashi
1/4 of the prize
b. 1944
Japan
Photo: Kyoto University
Toshihide Maskawa
1/4 of the prize
b. 1940
Japan
70
Cited 5527 times
71
CP-violation a la Kobayashi - Maskawa
1964 Cronin, Fitch, et al discovered: KL → π+ π– , which broke CP-symmetry.
CP-breaking makes particles behave differently
from their antiparticles:
Γ(KL → π − e+ ν̄e ) > Γ(KL → π + e− νe )
This makes it possible to distinguish
matter from antimatter.
CP-breaking requires the quark mixing
matrix to contain a complex phase.
A hug? Wait until the symmetry is
clarified first! If the alien being is made
of antimatter, a hug will result in both
of you vanishing in a puff of energy.
E.g., the 2x2 unitary Cabibbo-matrix
can, using suitable conventions, always
be expressed with the real parameter θC .
!
cos θC
− sin θC
sin θC
cos θC
"
72
CP-violation a la Kobayashi - Maskawa
Kobayashi and Maskawa proposed in 1973 that CP-could be understood if
there was a third generation of quarks, (t b). The unitary CKM-matrix which
expresses (d´, s´, b´) in terms of (d, s, b) is then a 3 x 3 matrix which allows a
complex parameter η:
where Vus ≈ sinθC ≈ λ.
The first indication of a 3. generation was the τ - lepton (Perl, 1975-77).
Lederman discovered the b-quark 1977.
The t-quark was found at Fermilab in 1994.
The CKM-matrix was now a strong candidate for explaining CP-violation.
This requires the vertex parameters Vij to form a unitary matrix.
73
The unitarity constraints, e.g.,
may be visualized as the requirements that the sum of the products Vij V*ik
form the sides of a triangle in the complex plane:
A determination of the matrix elements required the measurement av CPviolation in the decay of B-mesons (which contain a b-kvark).
74
Two “B-factories” were built, with the detectors:
Belle (KEK, Japan)
BaBar (SLAC, USA)
75
The data was
found to be
in perfect
agreement
with the
CKM-matrix!
76
Particle Data Group http://pdg.lbl.gov/
77
78
ΔΓ [10–18 GeV]
CPT symmetry requires–
equality of the K0 and K0
masses and widths
=0
=0
ΔM [10–18 GeV]
79
Abstract
80
Feynman rules
81

http://theory.physics.helsinki.fi/~qmii/

Transcription

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