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ScienceWeek
HISTORY OF PHYSICS: ON RENORMALIZATION IN QED
The following points are made by Freeman Dyson (Physics Today 2005 October):
1) From 2 to 4 June 1947, a carefully selected group of distinguished physicists assembled at Shelter Island, a small and secluded spot near the eastern tip of Long Island, to discuss the outstanding problems of physics. This was the first serious meeting of physicists who had played leading roles in World War II and then returned to the pursuit of peaceful science. The Shelter Island Conference succeeded in its purpose: It set the direction for physics for the next 30 years.
2) The main subject of discussion was the experiment of Willis Lamb and Robert Retherford, who used the tools of microwave spectroscopy, developed during the war for military purposes, to measure the fine structure of the energy levels of the hydrogen atom. The results showed a clear deviation of the observed levels from the predictions of the Dirac theory of the hydrogen atom. Lamb and Retherford measured a quantity that became known as the "Lamb shift" -- the frequency of a microwave field that induced transitions between the lowest two excited states of the hydrogen atom. According to the Dirac theory, the two states should have had equal energy and the Lamb shift should have been zero. Lamb measured it to be 1000 megahertz, with an uncertainty of a few percent. The discrepancy was far outside the limits of possible experimental error.
3) Many people at the conference, including Victor Weisskopf and Robert Oppenheimer, suggested that the deviation resulted from quantum fluctuations of the electromagnetic field acting on the electron in the atom. Such fluctuations would give the electron an additional energy, called the "self-energy". It was well known that the existing theory of quantum electrodynamics (QED) gave an infinite value for the self-energy and was therefore useless. Physics had reached an impasse. On the one hand, the Lamb experiment gave clear evidence that the effects of electromagnetic quantum fluctuations were real and finite. On the other hand, the existing theory of QED gave infinite and absurd results. It was obvious to everyone at the meeting that breaking the impasse would require a new idea.
4) Hendrik Kramers, one of the few non-US attendees, provided the new idea, which was named "renormalization". That name was already familiar to physicists in 1947; it had been used in a similar context by Robert Serber in 1936. Kramers had come from the Netherlands to spend a term as a visiting scientist at the Institute for Advanced Study in Princeton, New Jersey. He remarked that the observed energy of an electron according to QED is the sum of two unobservable quantities: a bare energy, which is the energy that an electron is supposed to have when it is uncoupled from electromagnetic fields, and the self-energy, which results from the electromagnetic coupling. The bare energy appears in the equations of the theory but is physically meaningless, since the electromagnetic coupling cannot really be switched off. Only the observed energy is physically meaningful. The point of renormalization was to get rid of bare energies and replace them with observed energies.
5) Kramers proposed that the results of the Lamb experiment should be calculated in terms of observed energies, with all mention of bare energies removed. He conjectured that when the bare energies were eliminated from the calculation, the infinite self-energies would cancel out and the calculated value of the energy difference that Lamb and Retherford measured would become finite. Kramers sketched a simple model of an electron for which the calculation could be done and the result was finite. But he did not know how to carry through the calculation for a real electron in a real hydrogen atom. Nobody at the meeting knew how to do a realistic calculation following Kramers's idea. Except Hans Bethe.[1-5]
References (abridged):
1. H. A. Bethe, Phys. Rev. 72, 339 (1947)
2. H. A. Bethe, E. Fermi, Z. Phys. 77, 296 (1932)
3. H. A. Bethe, Handbuch der Physik 24, 273 (1933)
4. H. A. Bethe, W. Heitler, Proc. Roy. Soc. London A146, 83 (1934)
5. H. A. Bethe, E. E. Salpeter, Phys. Rev. 84, 1232 (1951)
Physics Today http://www.physicstoday.org
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MATERIALS SCIENCE: SINGLE-ELECTRON-TRANSISTOR KONDO EFFECT
The following points are made by A. Kogan et al (Science 2004 304:1293):
1) The observation of the Kondo effect in nanometer-size semiconductor structures (1,2) has caused a renaissance in the study of this quantum mechanical many-body phenomenon. It has been known since the 1930s (3) that a small concentration of magnetic impurities in a metal radically changes the conductance at low temperatures. However, only with the development of scaling and renormalization group theory techniques could the equilibrium properties of this strongly interacting system be predicted.
2) The Kondo problem involves the coupling between an unpaired electron localized on an impurity and the surrounding delocalized electrons in a metal. The coupling leads to screening of the localized electron's spin by the delocalized electrons with opposite spin, so that a spin-zero singlet is formed below the Kondo temperature (TK). In 1988 it was proposed on the basis of theory (4,5) that a quantum dot containing an unpaired electron coupled to conducting leads would be analogous to a magnetic impurity coupled to its host metal.
3) Such a quantum dot coupled to two leads (the drain and the source), with a gate electrode nearby, is a single-electron transistor (SET). In the absence of the Kondo coupling, the conductance of a SET at zero drain-source bias (Vds = 0) is very small, except for values of the gate voltage at which two charge states of the quantum dot are degenerate. Thus, the zero-bias conductance as a function of gate voltage consists of a series of Coulomb charging peaks, one for each electron added to the dot. The Kondo effect enhances the conductance between these peaks when the dot contains a spin, because the screening of the spin creates a new spin-entangled many-electron quantum state that extends from one lead through the dot into the other lead.
4) SETs provide new ways of studying the Kondo effect that are not possible with magnetic impurities in metals. In particular, the capability of applying a voltage between the two leads of a SET makes it possible to study the Kondo effect out of equilibrium. It has been predicted that one such nonequilibrium phenomenon, photon-assisted Kondo conductance, should provide a new spectroscopy of the Kondo singlet.
5) In summary: The authors measured the differential conductance of a single-electron transistor (SET) irradiated with microwaves. The spin-entangled many-electron Kondo state produces a zero-bias peak in the dc differential conductance if the quantum dot in the SET contains an unpaired electron. When the photon energy (hf) is comparable to the energy width of the Kondo peak and to (e) (the charge on the electron) times the microwave voltage across the dot, satellites appear in the differential conductance shifted in voltage by +- hf/e from the zero-bias resonance. The authors also observe an overall suppression of the Kondo features with increasing microwave voltage.
References (abridged):
1. D. Goldhaber-Gordon et al., Nature 391, 156 (1998)
2. S. M. Cronenwett, T. H. Oosterkamp, L. P. Kouwenhoven, Science 281, 540 (1998)
3. A. C. Hewson, The Kondo Problem to Heavy Fermions, vol. 2 of Cambridge Studies in Magnetism (Cambridge Univ. Press, Cambridge, 1993)
4. L. I. Glazman, M. E. Raikh, JETP Lett. 47, 452 (1988)
5. T. K. Ng, P. A. Lee, Phys. Rev. Lett. 61, 1768 (1988)
Science http://www.sciencemag.org
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ON THE STANDARD MODEL AND A UNIFIED PHYSICS
Notes by ScienceWeek:
In particle physics, the "Standard Model" is a theoretical framework whose basic idea is that all the visible matter in the universe can be described in terms of the elementary particles leptons and quarks and the forces acting between them. Leptons are a class of point-like fundamental particles showing no internal structure and no involvement with the strong forces. Electrons and neutrinos are among the particles classified as leptons. The strong force (nuclear strong force) is one of the four fundamental forces: the gravitational force, the electromagnetic force, the nuclear strong force, and the nuclear weak force (see below), with the strong force approximately 100 times stronger than the electromagnetic force. A quark is a hypothetical fundamental particle, having charges whose magnitudes are one-third or two-thirds of the electron charge, and from which the elementary particles may in theory be constructed. At the present time, ongoing experimental projects in particle physics are expected to permit a completion of the Standard Model, but a unified theory of all forces known to physics is not yet in sight.
The following points are made by Steven Weinberg (Scientific American 1999 December):
1) In physics, the greatest advances of the past have been steps involving unification: a) the unification of terrestrial and celestial mechanics by Isaac Newton (1642-1727) in the 17th century; b) the unification of optics with the theories of electricity and magnetism by James Clerk Maxwell (1831-1879) in the 19th century; c) the unification of space-time geometry and the theory of gravitation by Albert Einstein (1879-1955) in the years 1905 to 1916; d) the unification of chemistry and atomic physics by quantum mechanics in the 1920s.
2) Our current theory of elementary particles and forces, known as the Standard Model of particle physics, has achieved a unification of electromagnetism with the weak interactions, the forces responsible for the change of neutrons and protons into each other in radioactive processes and in the stars. The Standard Model also gives a separate by similar description of the strong interactions, the forces that hold quarks together inside protons and neutrons, and that hold protons and neutrons together inside atomic nuclei. We have ideas about how the theory of strong interactions can be unified with the theory of weak and electromagnetic interactions, but the approach may only work if gravity is included, and the inclusion of gravity presents serious theoretical difficulties.
3) The Standard Model is a quantum field theory. Its basic ingredients are fields, including the electric and magnetic fields of 19th century electrodynamics. Perturbations in these fields carry energy and momentum from place to place, and quantum mechanics indicates these perturbations come in bundles, or quanta, which are recognized in the laboratory as elementary particles. For example the quantum of the electromagnetic field is the photon. The Standard Model includes a field for each type of elementary particle that has been observed in high-energy physics laboratories.
4) The Standard Model is a quantum field theory of a special kind, one that is "renormalizable". This term goes back to the 1940s, when physicists were learning how to use the first quantum field theories to calculate small shifts of atomic energy levels. They found that calculations using quantum field theory kept producing infinite quantities, a situation which usually indicates a theory is badly flawed or is being pushed beyond its limits of validity. Eventually, physicists discovered a way to deal with the infinite quantities by absorbing them into a redefinition, or "renormalization", of just a few physical constants, such as the charge and mass of the electron.
5) Although the profoundest advances in fundamental physics tend to occur when the principles of different types of theories are reconciled within a single new framework, we do not yet know what guiding principle underlies the unification of quantum field theory, as embodied in the Standard Model, with general relativity. The quantum nature of space and time must be dealt with in a unified theory. At the shortest distance scales, space may be replaced by a continually reconnecting structure of *strings and membranes -- or by something stranger still.
6) The author suggests it is impossible to state when these problems will be overcome. "They may be solved in a preprint put out tomorrow by some young theorist. They may not be solved by 2050, or even 2150. But when they are solved... we will not have any trouble in recognizing the truth of the fundamental unified theory. The test will be whether the theory successfully accounts for the measured values of the physical constants of the Standard Model, along with whatever effects beyond the Standard Model may have been discovered by then."
Scientific American http://www.sciam.com
ScienceWeek http://scienceweek.com
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