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

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

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 Quantum Mechanics II 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: Paul Hoyer Spring 2009 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 Quantum Mechanics II 3 Measurement of the muon magnetic moment Brookhaven National Lab., E821 http://www.g-2.bnl.gov/ Paul Hoyer Spring 2009 Quantum Mechanics II 4 gµ/2 = 1.0 011 659 214 (8)(3) e /2mµ α = 2π 0.0011614 Paul Hoyer Spring 2009 Quantum Mechanics II 5 Paul Hoyer Spring 2009 Quantum Mechanics II 6 Paul Hoyer Spring 2009 Quantum Mechanics II 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. Paul Hoyer Spring 2009 Quantum Mechanics II 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 Paul Hoyer Spring 2009 Quantum Mechanics II 9 Paul Hoyer Spring 2009 Quantum Mechanics II 10 http://arxiv.org/abs/0901.2505 _ 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. Paul Hoyer Spring 2009 Quantum Mechanics II 11 http://arxiv.org/abs/0901.2505 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. Paul Hoyer Spring 2009 Quantum Mechanics II 12 νe mass limits from decay measurements http://cupp.oulu.fi/neutrino/nd-mass.html Paul Hoyer Spring 2009 Quantum Mechanics II Physics Today November 2000 Recommended reading for QM II! Paul Hoyer Spring 2009 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 Quantum Mechanics II 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. Quantum Mechanics II 15 http://theory.physics.helsinki.fi/~qmii/Zeilinger_Nature.pdf Paul Hoyer Spring 2009 Nature June 2007 Quantum Mechanics II 16 Paul Hoyer Spring 2009 Quantum Mechanics II Nielsen and Chuang: Quantum Computation and Quantum Information, p. 532 Paul Hoyer Spring 2009 17 Quantum Mechanics II Nielsen and Chuang: Quantum Computation and Quantum Information, p. 532 Paul Hoyer Spring 2009 18 Quantum Mechanics II 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 Paul Hoyer Spring 2009 Quantum Mechanics II 20 From Sakurai: Modern Quantum Mechanics Paul Hoyer Spring 2009 Quantum Mechanics II 21 Physics Today, March 2002, page 20 ~qmii/QM+Gravity_PT55(02).pdf Paul Hoyer Spring 2009 Quantum Mechanics II 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. Paul Hoyer Spring 2009 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. Quantum Mechanics II 23 http://capp.iit.edu/hep/pbar/Phillips-GravityExpt.pdf Paul Hoyer Spring 2009 Quantum Mechanics II 24 http://capp.iit.edu/hep/pbar/Phillips-GravityExpt.pdf Paul Hoyer Spring 2009 Quantum Mechanics II 2008-12-05 Antimatter gravity experiment AEGIS approved at CERN in December 2008 Paul Hoyer Spring 2009 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 Quantum Mechanics II http://www.hitachi.com/rd/research/em/abe.html 26 Paul Hoyer Spring 2009 Quantum Mechanics II Verification of the Aharonov-Bohm effect Paul Hoyer Spring 2009 27 http://www.hitachi.com/rd/research/em/abe.html Quantum Mechanics II 28 Paul Hoyer Spring 2009 Quantum Mechanics II 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 Quantum Mechanics II • 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 Quantum Mechanics II 31 Physical Review A7 (1973) 1224 Charge of SF6 molecule is less than 2⋅10–19 e |ep+ee| < 1⋅10–21 ee Paul Hoyer Spring 2009 Quantum Mechanics II 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 " Paul Hoyer Spring 2009 = (−1)J−j1 −j2 !j2 j1 m2 m1 |j2 j1 JM " Quantum Mechanics II 33 Paul Hoyer Spring 2009 Quantum Mechanics II 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). Paul Hoyer Spring 2009 Quantum Mechanics II 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) Paul Hoyer Spring 2009 l=4 r/a0 Quantum Mechanics II 37 "#$%&' (&#)$*+#,%&-,&-./0 Atoms http://www.itkp.uni-bonn.de/~rusetsky/TRENTO06/talks.html n 4 3 s p d E2p 2 "1s 1 !# f [email protected]%0(A%D8A25% [email protected]%6202)6%(E= ()7>878B>) !$%%%&%%'()%"#$ !%& '()*+,%&-.#/&01(2 )*+,%&-#0.01 } !1s E1s 4')%23%25)%6213(7%8(2)109283(%:03(;<1323( 25)%=6%>)?)>%86%[email protected])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 Paul Hoyer Spring 2009 Quantum Mechanics II 39 From F. S. Levin, p. 708 Paul Hoyer Spring 2009 Quantum Mechanics II 40 From F. S. Levin, p. 712 Paul Hoyer Spring 2009 Quantum Mechanics II 41 From F. S. Levin, p. 721 Paul Hoyer Spring 2009 Quantum Mechanics II 42 Paul Hoyer Spring 2009 Quantum Mechanics II 43 Paul Hoyer Spring 2009 Quantum Mechanics II 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 Paul Hoyer Spring 2009 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 Quantum Mechanics II 45 This historical review of the discovery of parity violation may be found at: http://ccreweb.org/documents/parity/parity.html Paul Hoyer Spring 2009 Quantum Mechanics II 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. Paul Hoyer Spring 2009 http://musr.org/~jess/musr/cap/pidk.htm Quantum Mechanics II http://www.mpi-hd.mpg.de/hfm/CosmicRay/Showers.html Paul Hoyer Spring 2009 47 Quantum Mechanics II 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 Paul Hoyer Spring 2009 Quantum Mechanics II 49 www.physics.indiana.edu/~charlie/parity/talks/bouchiat.ps.gz Paul Hoyer Spring 2009 Quantum Mechanics II 50 http://en.wikipedia.org/wiki/Electronic_band_structure Comparison of the electronic band structures of metals, semiconductors and insulators Paul Hoyer Spring 2009 Quantum Mechanics II 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. Paul Hoyer Spring 2009 Quantum Mechanics II http://en.wikipedia.org/wiki/Neutron_electric_dipole_moment52 Paul Hoyer Spring 2009 Quantum Mechanics II http://www.cambridge.org/resources/052182379X/2064_ch06.pdf Paul Hoyer Spring 2009 53 Quantum Mechanics II Lattice waves http://en.wikipedia.org/wiki/Phonon 54 Diagonalized Collection of N+1 independent harmonic oscillators, labelled by k Paul Hoyer Spring 2009 For each k, state is labelled by number nk of phonons Quantum Mechanics II http://www.cambridge.org/resources/052182379X/2064_ch06.pdf Paul Hoyer Spring 2009 55 Quantum Mechanics II http://www.cambridge.org/resources/052182379X/2064_ch06.pdf 56 Phonons, photons, pions can be created and annihilated in scattering _ e+e– → q q g : Paul Hoyer Spring 2009 γ* Feynman diagram Quantum Mechanics II http://www.lnf.infn.it/~levisand/graal/graal_beam_intro.html 57 Backscattered photon beam at ESF (Grenoble): 6 GeV electrons against laser photons Paul Hoyer Spring 2009 Quantum Mechanics II 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. Paul Hoyer Spring 2009 Picture taken from C.D. Anderson, Physical Review 43, 491 (1933). Quantum Mechanics II http://teachers.web.cern.ch/teachers/archiv/HST2005/bubble_chambers/BCwebsite/index.htm 59 Bubble Chamber Paul Hoyer Spring 2009 Quantum Mechanics II 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. Paul Hoyer Spring 2009 Quantum Mechanics II 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 . Paul Hoyer Spring 2009 Quantum Mechanics II 62 The QED experience Paul Hoyer Spring 2009 Quantum Mechanics II 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?” Paul Hoyer Spring 2009 Quantum Mechanics II 64 Paul Hoyer Spring 2009 Quantum Mechanics II Bound states of atoms Paul Hoyer Spring 2009 U.D. Jentschura et al, PRL 95 (2005) 163003 65 Quantum Mechanics II 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 Paul Hoyer Spring 2009 Quantum Mechanics II http://home.fnal.gov/~prebys/talks/rochester_20010926.pdf Paul Hoyer Spring 2009 67 Quantum Mechanics II 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 Paul Hoyer Spring 2009 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 Quantum Mechanics II "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 Paul Hoyer Spring 2009 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 Quantum Mechanics II 70 Cited 5527 times Paul Hoyer Spring 2009 Quantum Mechanics II 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 . ! Paul Hoyer Spring 2009 cos θC − sin θC sin θC cos θC " Quantum Mechanics II 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. Paul Hoyer Spring 2009 Quantum Mechanics II 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: Paul Hoyer Spring 2009 Quantum Mechanics II 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) Paul Hoyer Spring 2009 Quantum Mechanics II BaBar (SLAC, USA) Paul Hoyer Spring 2009 75 Quantum Mechanics II The data was found to be in perfect agreement with the CKM-matrix! Paul Hoyer Spring 2009 76 Quantum Mechanics II Particle Data Group http://pdg.lbl.gov/ Paul Hoyer Spring 2009 77 Quantum Mechanics II 78 ΔΓ [10–18 GeV] CPT symmetry requires– equality of the K0 and K0 masses and widths Paul Hoyer Spring 2009 =0 =0 ΔM [10–18 GeV] Quantum Mechanics II http://arxiv.org/abs/0809.2846 79 Abstract Paul Hoyer Spring 2009 Quantum Mechanics II 80 Feynman rules Paul Hoyer Spring 2009 Quantum Mechanics II 81 Paul Hoyer Spring 2009 Quantum Mechanics II