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ESI NEWS Volume 3, Issue 2, Autumn 2008 The Erwin Schrodinger¨ International Boltzmanngasse 9/2 Institute for Mathematical Physics A-1090 Vienna, Austria ESI NEWS Volume 3, Issue 2, Autumn 2008 Editorial final report of the evaluation was sent to the Austrian Ministry of Science in June 2008. Contents Klaus Schmidt Apart from praising the quality of the Editorial 1 programmes which had taken place at the The 15th anniversary Nobel Prize in Physics 2008 2 ESI during the past five years, he review the ESI in April 2008 panel noted that the Institute had ‘gen- Metastability and Rare Events in was an occasion not tly and wisely’ increased its scope of the Complex Systems 4 only for celebration, programmes in recent years, into areas of but also for an evalu- pure mathematics more remote at present Josef Stefan, Josef Loschmidt and ation of the Institute’s Stigler’s Law 7 from theoretical physics, and into areas of performance over the physics and biology beyond those usually Remarks on Boltzmann’s Philoso- past 5 years and its characterized as mathematical physics. The phy 8 scope for future development. panel felt that this process should be con- The previous evaluation of the ESI ESI News 12 tinued in the same judicious fashion as in in 2003 had been chaired by Nigel recent years. Current and Future Activities of Hitchin (Oxford), who had recruited as The report also contains a number of the ESI 13 co-evaluators Robbert Dijkgraaf (Ams- terdam), Jurgen¨ Jost (Leipzig), Nicolai recommendations for the development of Schrodinger¨ Lectures 2008/2009 15 Reshetikhin (Berkeley) and Vincent Ri- the ESI over the next years. These pro- posals and their financial implications are Senior Research Fellows’ Lecture vasseau (Orsay). currently under further discussion with the Courses 2008/2009 15 The evaluation in 2008 followed essen- tially the same pattern: Peter Goddard (IAS University of Vienna and the Austrian Min- Workshop on Mathematics at the Princeton) agreed to chair the evaluation istry of Science. Turn of the 20th Century 15 and chose for his panel of co-evaluators Jean-Michel Bismut (Orsay), Robbert Di- On behalf of the Erwin Schrodinger¨ In- jkgraaf (Amsterdam), Felix Otto (Bonn) stitute I would like to send seasons greet- and Scott Sheffield (Courant Institute). Af- ings and my best wishes for a happy and ter a site visit by the panel in April 2008 the peaceful year 2009. EVALUATION OF THE ESI, APRIL 2008 The scientific directors of the ESI, Joachim Schwermer and Jakob Yngvason, together with the evaluators Peter Goddard (IAS Princeton, chair), Scott Sheffield (Courant Institute), Jean-Michel Bismut (Orsay) and Felix Otto (Bonn) – from left to right. 2 Volume 3, Issue 2, Autumn 2008 ESI NEWS Nobel Prize in Physics Till the middle of the last century, symme- The main inspiration for Nambu came try principles were thought to express the from the BCS theory of superconductivity 2008: Symmetry Violation basic simplicity of nature. The discovery [2]. In certain metals, the electron-phonon in Subatomic Physics that some of the “sacred” symmetries such interaction can lead to the formation of as parity (P), time reversal or charge con- Cooper pairs (two electrons with opposite Gerhard Ecker and Walter Grimus jugation (C) were only approximate came momenta and spins) that condense in the therefore as a surprise. In his Nobel Lec- ground state. The ground state is there- tures of 1979 Weinberg expressed this feel- fore charged implying the spontaneous vi- The No- ing as a question: “Is nature only approxi- olation of gauge invariance. In an impor- bel Prize in mately simple?” By now there is a general tant paper [3], Nambu demonstrated that Physics 2008 consensus that also approximate symme- gauge invariance, although not manifest in was awarded tries may reveal fundamental properties of the BCS theory, is nevertheless fully main- to Yoichiro nature. For instance, CP violation is essen- tained. Nambu (Enrico tial for the baryon asymmetry of the uni- That was the starting point for Nambu Fermi Institute, verse and thus for our existence [1]. and Jona-Lasinio to investigate the struc- Chicago, USA) for “the discovery of the Symmetries in particle physics can be clas- ture of the ground state in relativistic mechanism of spontaneous broken symme- sified in four groups: quantum field theories relevant for parti- try in subatomic physics” and to Makoto cle physics. The Lagrangian of the Nambu– Kobayashi (KEK, Tsukuba, Japan) and 1. Exact symmetries leave the field Jona-Lasinio (NJL) model [4] Toshihide Maskawa (Yukawa Institute for equations and the ground state µ Theoretical Physics, Kyoto, Japan) for “the of the theory invariant. Examples LNJL = γ i@µ + are the Poincare´ transformations discovery of the origin of the broken sym- metry which predicts the existence of at (Lorentz transformations and space- g0 − γ5 γ5 time translations) and the gauge least three families of quarks in nature.” describes the self-interaction of a single nu- symmetries of electromagnetic and cleon field and is modeled after the BCS strong interactions. Symmetries in physics Lagrangian. Because of the absence of a The modern view of symmetries as groups 2. Spontaneously broken symmetries mass term m the Lagrangian and the of transformations that leave the equations still leave the field equations invari- field equations are invariant with respect of motion invariant emerges in the 19th ant, but not the ground state. Nambu to two independent phase transformations century. With the advent of quantum me- was the first to realize the impor- (chiral symmetry) chanics in the 1920s, symmetries were tance of this concept in relativistic (x) ! eiα (x); (x) ! eiβγ5 (x) : found to explain degeneracies in spectra quantum field theories. Examples are and to give rise to relations between mea- the chiral symmetry of the strong in- Depending on the size of the coupling surable quantities such as cross sections teractions (in the limit of vanishing constant g , the ground state of the the- and decay rates. In addition to the classical 0 quark masses) and the electroweak ory may exhibit spontaneous breakdown of space-time symmetries (Galilei, Poincare),´ gauge symmetry. the chiral symmetry, generating both a fi- a new type of symmetries occurs in quan- nite mass for the initially massless nucleon tum field theories: the so-called “internal” 3. Approximate symmetries do not and a massless collective excitation (pion). symmetries do not affect space and time even leave the field equations in- The modern version of the NJL model but they transform the fields of the theory. variant, but traces of the symme- is Quantum Chromodynamics (QCD), the The gauge symmetries of the fundamental tries are still visible in measurable gauge theory of quarks and gluons for the interactions are prominent examples. quantities. Symmetries violated only strong interaction. Chiral symmetry holds by the weak interactions (P, CP, Symmetries play an important role in sub- for massless quarks, which is a good ap- strangeness, . ) are of this type. atomic physics: proximation for the two lightest quarks Kobayashi and Maskawa received u; d. Spontaneous breaking of chiral sym- i. Unlike gravitational and electromag- the Nobel Prize for their explanation metry provides the only plausible expla- netic forces, nuclear forces are re- of CP violation in the SM. nation why pions are by far the lightest mote from our everyday experience. hadrons. From the study of spectra and other 4. Anomalous symmetries leave the observables, physicists extract clues classical field equations invariant, In the NJL model, most of the nucleon for underlying symmetries to be but are violated by quantum effects. mass arises from spontaneous chiral sym- implemented in the corresponding metry breaking. According to our present quantum field theories. Spontaneous symmetry breaking understanding, the small u and d masses The notion of spontaneous symmetry contribute actually only about 5% to the ii. Theoretical physics often proceeds breaking originated in solid state physics. nucleon mass. In other words, 95% of our by analogies and extrapolations: ex- For example, the Hamiltonian describing a mass and of the visible universe are due to tending the gauge symmetry of the ferromagnet is rotationally invariant in the the strong quark-gluon interaction in QCD. electromagnetic interaction to the absence of an external magnetic field, yet Only the small remainder requires a differ- weak and strong interactions led the ground state exhibits spontaneous mag- ent mechanism for mass generation. to the modern theory of the fun- netization along some arbitrary direction: Inspired by the work of Nambu and Jona- damental interactions, the Standard rotational symmetry is spontaneously bro- Lasinio, Goldstone demonstrated [5] that Model (SM) of particle physics. ken in the ferromagnet. spontaneously broken symmetries lead to Erwin Schrodinger¨ Institute of Mathematical Physics http://www.esi.ac.at/ ESI NEWS Volume 3, Issue 2, Autumn 20083 massless excitations in general. In the case V–A (vector minus axial vector current) Hamiltonian density is given by of so-called global symmetries (e.g., chi- theory of weak interactions in which both ral symmetries), these excitations would be P and C are maximally violated. Hcc = massless particles (pions for mu = md = g µ + In the V–A theory, CP was conserved in p u¯γ (1 − γ5)V d W + H.c. ; 0). As shown a few years later by Brout µ a natural way. Therefore, the discovery 2 2 and Englert [6] and by Higgs [7], the situ- + of the decay K ! π+π− in 1964 at where W is the W-boson field, g is the ation is different for gauge symmetries (lo- L the Brookhaven National Laboratory [8], SU(2) gauge coupling constant and u and cal symmetries): the Nambu-Goldstone ex- a manifestation of CP violation, was com- d are the column vectors containing the citations are not physical particles but they pletely unanticipated and provided a new quark fields with charge 2=3 and −1=3, re- render some of the initially massless gauge puzzlement which did not diminish with spectively.
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