Symmetry Principles and Conservation Laws in Atomic and ...
Symmetry Principles and Conservation Laws in Atomic and ...
Symmetry Principles and Conservation Laws in Atomic and ...
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GENERAL ARTICLEThe perturbative expansion about one of the two m<strong>in</strong>imahas led to a real mass appear<strong>in</strong>g. S<strong>in</strong>ce the expansionis made about one or other of the m<strong>in</strong>ima, chosenat r<strong>and</strong>om, the symmetry of Figure 5 is broken. This isthe process of spontaneous symmetry break<strong>in</strong>g.Nambu <strong>and</strong> Jona-Las<strong>in</strong>io ¯rst applied spontaneous symmetrybreak<strong>in</strong>g as mechanism of mass generation <strong>in</strong> 1961.In recognition of this work Nambu was awarded a shareof the 2008 Nobel Prize [9]. There are many examplesof spontaneous symmetry break<strong>in</strong>g <strong>in</strong> other areas ofphysics. For example a bar magnet heated above theCurie temperature has its elementary magnetic doma<strong>in</strong>sorientated r<strong>and</strong>omly, lead<strong>in</strong>g to zero net ¯eld. The Lagrangi<strong>and</strong>escrib<strong>in</strong>g the ¯eld of the magnet would be<strong>in</strong>variant under rotations. However, on cool<strong>in</strong>g, the doma<strong>in</strong>sset <strong>in</strong> a particular direction, caus<strong>in</strong>g an overall¯eld <strong>and</strong> break<strong>in</strong>g the rotational symmetry. Thereare further examples of spontaneous symmetry break<strong>in</strong>g<strong>in</strong> the description of superconductivity; these <strong>in</strong>spiredNambu <strong>and</strong> Jona-Las<strong>in</strong>io's work <strong>in</strong> particle physics.The <strong>in</strong>troduction of such a scalar ¯eld <strong>in</strong>teraction <strong>and</strong>a spontaneous symmetry break<strong>in</strong>g with<strong>in</strong> the st<strong>and</strong>ardmodel allows the weak force carry<strong>in</strong>g bosons, W § <strong>and</strong>Z 0 , to obta<strong>in</strong> mass as well as all quarks <strong>and</strong> leptons. Inaddition, this leads to the physical Higgs boson. TheHiggs boson is the only part of the st<strong>and</strong>ard model ofparticle physics that has not been experimentally veri-¯ed. However, the precise measurements of the propertiesof the Z 0 <strong>and</strong> the W § by experiments at theLarge Electron Positron (LEP) collider, which operatedat the European Centre for High Energy Particle Physics(CERN) <strong>in</strong> Geneva, Switzerl<strong>and</strong>, <strong>and</strong> of the W § <strong>and</strong> theheaviest quark (the top) at Fermilab, have led to an upperlimit on the mass of the Higgs boson of 157 GeV=c 2with a 95% con¯dence level. In addition, unsuccessfulsearches for the production of a st<strong>and</strong>ard model Higgsboson at LEP placed a lower limit on the mass of theNambu <strong>and</strong> Jona-Las<strong>in</strong>io first appliedspontaneoussymmetry break<strong>in</strong>gas mechanism ofmass generation <strong>in</strong>1961. In recognitionof this work Nambuwas awarded a shareof the 2008 NobelPrize.The Higgs boson isthe only part of thest<strong>and</strong>ard model ofparticle physics thathas not beenexperimentallyverified.RESONANCE October 2010937
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