New Trends in Mathematical Physics: Selected contributions of the XVth International Congress on Mathematical Physics

885 Pages·2009·14.629 MB·English

by  Nalini Anantharaman, Herbert Koch (auth.), Vladas Sidoravičius (eds.)

New Trends in Mathematical Physics
Vladas Sidoravicˇius
Editor
New Trends
in Mathematical Physics
Selected Contributions
of the XVth International Congress
on Mathematical Physics
VladasSidoravicˇius
InstitutodeMatemáticaPuraeAplicada(IMPA)
EstradaDonaCastorina110
RiodeJaneiro,RJ
Brazil
[email protected]
ISBN978-90-481-2809-9 e-ISBN978-90-481-2810-5
DOI10.1007/978-90-481-2810-5
SpringerDordrechtHeidelbergLondonNewYork
LibraryofCongressControlNumber:2009932135
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Preface
The XV-th International Congress on Mathematical Physics took place in Rio de
Janeiro, on August 5–11, 2006. I believe it was a very successful and enjoyable
meeting.ItisveryfortunateforourcommunitythatLatinAmerica,andespecially
Brazil, in decades has become the place where all fields of intellectual activity
which are traditionally regarded as part of Mathematical Physics are developing
withsteadypaceandremarkablequality.Anotherimportantaspectofthisdevelop-
mentisthatbesidesareaswhichalreadyhaveworldwiderecognitionandlongstand-
ingtraditioninBrazilsuchasDynamicalSystems,StatisticalMechanics,Probabil-
ityTheory,etc.,thereisintensivegrowthinotherdirectionssuchasStringTheory
andAlgebraicGeometry.Brazil’smajoruniversitiesandresearchinstitutessuchas
IMPAandCBPFaresuccessfullybringingupanewgenerationofresearchersinour
field.Thusitwasespeciallypleasanttoseethatamongmorethan500participants
of the Congress, the majority was constituted by young researchers and graduate
students.
GiventheenormousrangeofsubjectscoveredduringtheCongress,andthedi-
versity of scientific contributions, it would be pointless to summarize the contents
here—thequalityisreflectedinthesepages.
Traditionally, besides its very intense scientific program, the Congress was the
occasion for the award of the Henri Poincaré Prizes of the IAMP, sponsored by
the Daniel Iagolnitzer Foundation. The Laureates for the year 2006 were Ludwig
Faddeev,DavidRuelleandEdwardWitten.
As with any other period between successive IAMP Congresses, this one was
witnessingscientificexcitementandimportantdevelopmentsinmanyareas.Perel-
man’s proof of the Poincaré conjecture and progress in geometrization program
were the central topic of many discussions, seminars, talks and meetings. I also
wouldliketomentionthespectaculardevelopmentsintheareaofRandomMatri-
cesandtheprogressmadebyF.GuerraandM.Tallagrandinspin-glasses.Perhaps
itwouldnotbeanexaggerationtosaythatthedevelopmentofStochasticSchramm-
Loewner Evolution and understanding of two-dimensional critical systems and its
connectionswithConformalFieldTheorycontinuetobeoneofthemostfascinating
chaptersofcontemporaryProbabilityTheoryandStatisticalMechanics.Afewdays
v
vi Preface
aftertheCongressinRio,WendelinWerner,theplenaryspeakeroftheXVthICMP,
was awarded the Fields medal for his contribution to this field. And in the spring
of 2007 Srinivasa Raghu Varadhan, the chair of the International Scientific Com-
mitteeoftheXVICMP,wasawardedtheAbelPrize.Ibelievethisspeaksnotonly
abouttherecognitionoftheincreasingroleofProbabilityTheoryandappreciation
of its mathematical depth, but also about importance of all our community, since
researchperformedbyW.WernerandS.R.Varadhan,andtheoriginsofquestions
theyanswer,aredeeplyrootedinthefieldsofMathematicalPhysics.
HoweveritwasalsothetimewhenwithgreatsadnesswelearnedinSeptember
2008abouttheuntimelydeathofOdedSchramm,theinventorofSLEandthe2003
PoincaréPrizerecipient.
ThepreparationoftheCongressasusualhastakenahugeamountofwork.On
thescientificsideImustthankallthemembersoftheInternationalScientificCom-
mittee.IwouldlikealsotoexpressmydeepgratitudeandaffectiontoDavidBry-
dges,thePresidentofInternationalAssociationofMathematicalPhysicsduringthe
period2003–2005,whowasthevisionary,drivingforceandfirstaidhelpatalloc-
casions.AmongthelocalorganizersIhavetosingleoutfirstofallProf.J.F.Perez
andProfs.C.Camacho,J.PalisandM.Vianawhowerepivotalforthesuccessof
themeeting.Andlastbutnoleast,allmythanksandappreciationtothewholeteam
of logistic and administrative support of DAC, masterfully conducted by Mme. S.
Lima.
TheCongresscouldnothavehappenedwithoutthegeneroussupportofnumer-
oussponsorsandeffortsofmanyindividuals,whoarelistedonthehomepageofthe
congress(http://www.iamp.org/).I’mmostgratefultothemall.Thereaderalsowill
findtherethelistofparticipantsofthemeeting.
Finally a few words on the organization of the book. We were not seeking to
produce a standard “Proceedings” book. To document the content of the plenary
talks and invited talks in all specialized sessions, in the Appendix to the book we
include the abstracts of the meeting as they stood in August 2006, so that the in-
terestedreadercan tracebackthecontentsof alltalks.As for themainpartof the
book, we invited all plenary speakers and invited speakers of specialized sessions
to contribute with articles that they find appropriate for this volume,reflecting the
current state of the art in Mathematical Physics, and which are written according
to their own vision of the developmentof their fields.Thus, as a result, the reader
will find here the original research articles,extensivereviews, as well as extended
versionsoftalks.
VladasSidoravicˇius
Foreword
MathematicalPhysicshasonoccasionweatheredthelabelofbeingacurioussub-
set of Theoretical Physics confined to “esoteric” questions such as exchanges of
limits,measurabilityofsets,existenceofsolutionstoequations,inotherwords,an
obsession with issues that deserve little or no mention at all. In my view this is a
destructiveattitudeandithastobemadeclearthatthedistinctionshouldbe,andis,
betweeninterestingandnotinterestingorphysicallyrelevantandirrelevantandthat
thereisavirtueintheclearformulationofproblemsandacleardistinctionbetween
assumptionsandresults.
Itisafactthatthesegoalshavenotgeneratedanydamagetoresearch,asthemain
andbestknowncontributionstoPhysicaltheoriesprove(PtolemaicandCopernican
astronomy, Keplerian and Newtonian mechanics, ergodic hypothesis, electromag-
netism,relativity,quantummechanics,condensedmatter,quantumfieldtheory,sta-
bilityofmatter,symmetriesinatomicandparticlePhysics,...):thekeyworks,even
when not formulated in mathematical terms, have always kept an extremely lucid
distinction between assumptions and consequences and have been influential and
recognizedbyall.
Neverthelesstheabovementionedattitudeshaveledtoproblemsthatinevitably
generate difficulties in jobs hiring, obtaining grants, priority recognition, impact
factorcomparison,andmore:sothatIAMPhasthescopeofhelpingtheratherlarge
communitythatlooksatproblemsandsubjectstheiranalysistorigorouscriticism.
Intheendthisamountstoadistinctionbetweenhypotheses,deductionsandresults
whenreading the “bookof Nature”,whichis recognizedby all of us, withGalilei
andhispredecessorsandfollowers,tobewritteninmathematicalcharacters.
TheICMP’smeetingshavebeendesignedtoinformalloftheIAMPmembersof
thestatusofourwork,toprovidetotheentirePhysicscommunityevidenceofthe
relevanceoftheresultsandtoshowthecloseinterestthatwepaytotheevolution
ofTheoreticalPhysics.
The Rio meeting is the most recent example of the width of the interests and
theopenmindednessofitsmembers.Aglimpseattheconferencetitlesshowsthat
the most varied subjects have been presented in the plenary talks and in the par-
allel sessions. From geometry, to string theory, to general relativity, to statistical
vii
viii Foreword
mechanicsinequilibrium(classicalandquantum)andnonequilibriumfluctuations,
todynamicalsystems,tosymmetries,toPDE’s....
The three Henri Poincaré prizes, that the Iagolnitzer Foundation sponsors and
theIAMPawards,recognizeexceptionalcontributionsandhonorthreecolleagues,
fortheirgreatcontributionstoPhysicsandforprovidingexamplesthatwewilltry
toimitateonhowtolookatproblemsthatwecherish.
Wethinkthatthewidevarietyofsessionandplenarytalkswillprovide,through
the publication of the present proceedings, inspiration for new challenging prob-
lems,andconfidence,tothemanyyoungcolleagueswhowanttocontinuetheex-
citingexperienceofthoseofuswhohavefollowedthedevelopmentsfromtheearly
‘960’s and can feel the immense difference between what was known at the time
andtoday.
FinallyIAMPthanksthelocalorganizersofthemeetinginRiofortheeffortthey
madetomakeeasyandagreeableparticipationbyourcolleagues,particularlythose
whoundertookalongjourneytoattendourmeeting.
It has been decided that ICMP09 will be held in Prague and we are sure that it
will continue the tradition of excellence that this and earlier ICMP meetings have
bequeathedtous.
GiovanniGallavotti
IAMPPresident2006–2008
IAMPPresidents
DavidBrydges(Vancouver),FormerIAMPPresident
GiovanniGallavotti(Rome),FormerIAMPPresident
PavelExner(Prague),CurrentIAMPPresident
InternationalScientificCommittee
D.Brydges(Vancouver)
G.M.Graf(Zürich)
G.Huisken(Tübingen)
A.Its(Indianapolis)
V.Schomerus(Saclay)
V.Sidoravicˇius(RiodeJaneiro)
S.R.S.Varadhan(Chairman)(NewYork)
SessionOrganizers
J.Baik(AnnArbor) R.Longo(Rome)
N.Berkovits(SãoPaulo) F.Martinelli(Rome)
J.Cardy(Oxford) W.deMello(RiodeJaneiro)
P.Chrusciel(Tours) S.Mueller(Leipzig)
R.Dijkgraaf(Amsterdam) B.Nachtergaele(Davis)
W.E.(Princeton) C.M.Newman(NewYork)
K.Fredenhagen(Hamburg) H.Nicolai(Golm)
J.Harnad(Montréal) M.B.Ruskai(Medford)
A.Holevo(Moscow) I.M.Sigal(Toronto)
G.Jona-Lasinio(Rome) B.Simon(Pasadena)
A.Laptev(Stokholm) F.Smirnov(Paris)
F.Ledrappier(NotreDame) J.P.Solovej(Copenhagen)
ix
x
NationalOrganizingCommittee
C.AragãodeCarvalho,RiodeJaneiro D.H.U.Marchetti,SãoPaulo
R.Dickman,BeloHorizonte A.OsóriodeAlmeida,RiodeJaneiro
R.Exel,Florianópolis M.O’Carroll,SãoCarlos
P.A.FariadaVeiga,SãoCarlos E.A.Pereira,BeloHorizonte
P.A.Ferrari,SãoPaulo J.FernandoPerez,SãoPaulo
L.A.Ferreira,SãoPaulo R.Schonmann,SãoPaulo
M.Forger,SãoPaulo R.Schor,BeloHorizonte
H.Frid,RiodeJaneiro V.Sidoravicˇius,RiodeJaneiro(Chairman)
A.Galves,SãoPaulo M.E.Vares,RiodeJaneiro
C.Grebogi,SãoPaulo M.Viana,RiodeJaneiro
C.Landim,RiodeJaneiro J.Zubelli,RiodeJaneiro
P.A.Letelier,Campinas
ICMP2006—InternationalAdvisoryCommittee
C.Dafermos(Brown) C.Newman(Courant)
J.Feldman(VBC,Vancouver) D.Olive(Swansea,Wales)
K.Fredenhagen(Hamburg) E.Presutti(RomaII)
J.Frohlich(ETH,Zurich) V.Rivasseau(Polytechnique)
K.Gawedzki(ENS,Lyon) C.Rogers(NewSouthWales)
A.Jaffe(Harvard) D.Ruelle(IRES)
G.Gallavotti(RomaI) B.Simon(Caltech)
G.Jona-Lasinio(RomaI) H.Spohn(TV,Munich)
V.Jones(Berkeley) A.-S.Sznitman(ETH,Zurich)
J.Lebowitz(Rutgers) J.-C.Zambrini(Lisbon)
E.Lieb(Princeton)
xi
TheXVInternationalCongressonMathematicalPhysicswasorganizedbytheIn-
ternationalAssociationofMathematicalPhysics(IAMP),inassociationwithInsti-
tutoNacionaldeMatemáticaPuraeAplicada(IMPA),RiodeJaneiro,Institutodo
Milênio(IM-AGIMB)andPetrobras(Brazil).
PastCongresses
Moscow(Russia),1972 Marseille(France),1986
Warsaw(Poland),1974 Swansea(UnitedKingdom),1988
Kyoto(Japan),1975 Leipzig(Germany),1991
Roma(Italy),1977 Paris(France),1994
Lausanne(Switzerland),1979 Brisbane(Australia),1997
Berlin(Germany),1981 London(UnitedKingdom),2000
Boulder(USA),1983 Lisbon(Protugal),2003