Mul$ple Reﬂec$ons, 23 May, 2016 · Life at Harvard in 1970’s • Robert led an unconven$onal life. • His friend Christa, whom he met on a skiing trip, was East German

Mul$pleReflec$ons,23May,2016

ThreeStagesofReflec$on

•  Somereflec$onsonRobert•  Somereflec$onsonreflec$onposi$vity•  Somereflec$onsaAerRobert

23May2016 Mul$pleReflec$ons 2

Reflec$onsonRobert

•  IfirstmetRobert48yearsagoinMay1968–  IwasguestprofessoratETH,courtesyJostandHepp– Robertwasworkingonhisthesis,completed1969– KonradOsterwalderwasmyassistant


Robert Konrad

SeminarfürTheore$schePhysik

Hochstrasse60

Zürich

Reflec$onsonRobert•  RobertcametoHarvardasmyfirstpost-doctoralfellowinthefallof1970(easytoarrange)•  Wespentthespring1971togetherinPrinceton.•  FirstprojectwasinfinitevolumelimitofYukawa2.•  Konradjoinedusinfall1971atHarvardaspost-d.


LifeatHarvardin1970•  RobertlivedonHuronAvenuein“westCambridge.”•  Hebecamegoodfriendswiththepar$clephysicists:ShellyGlashow,SidneyColeman,andJohnIliopolous($meofGIMmechanism).

•  Manyunmarriedfaculty:Coleman,Glashow,AJ.Facultyandpostdoctoralfellowssocializedalot,occasionallyalsoCallan,Gross,Mar$n,Glauber,Schwinger.

•  RegularSundaylunchatthePekingonMys$c.


LifeatHarvardin1970’s•  Robertledanunconven$onallife.•  HisfriendChrista,whomhemetonaskiingtrip,wasEastGerman.SoRobertoAenwenttovisit.

•  TheStasiaeemptedtorecruitRobertasaspy,interroga$nghimandthreateningherfamily.

•  RobertwantedtogetChristatotheWestlegally.Igotintothemiddleofthatmess,theFBIgotinvolved,andsodidtheGermangovernment.

•  Thistook5years,2kids,andalotofmoney.•  In1992,aAerthewallcamedown,IgaveatalkinBerlin.Roberttookmetoseetheprison(thenamuseum)wherehehadbeeninterrogatedsome20yearbefore.


Reflec$onsonReflec$onPosi$vityOntheDiscovery

•  Summer1972,Roberthadgoneonvaca$ontovisitChrista.•  IbegandiscussingwithKonradthepaperofEdwardNelsononMarkov

fieldreconstruc$on.•  Iwasinterestedtoknowiftherewasabasicprinciplethatworked

independentoftheMarkovproperty,andmightapplytoothersitua$ons.

•  ThenRobertcamebackfromhisvaca$on.•  HehadleAhiscarinNorthampton,whereIhadanapartment.There

onecouldparkonthestreetwithoutlimitof$me.•  IdroveRoberttopickuphiscar.Wehadaveryinteres$ng2-hour

trip!•  IleAfromNothamptontoChicagoforaconference.•  WhenIreturnedtoBoston4dayslater,O&ShaddiscoveredRP!•  Wri$ngituptookalmosttwoyears.•  Iwasdeeply$edupinmyworkonclusterexpansionsandonthree

dimensions.


Reflec$onsonReflec$onPosi$vityWhatisRP?


– BasicSchrödingerEqua$on:

– Hamiltonian(Energy).Wantstability:

– Ensuresanaly$cityinacomplexhalft-plane.

i}@ @t = H

H > 0

ModifyEqua$on:Con$nueanaly$callyintHeatDiffusionEqua$on:

Imaginary(unphysical)$me:Easiertostudy,BUT:Ques$on:Howcanonegetback?Answer:RP.18May2016 DIASSTPSPL 10

�}@ @t = H

t ! �it

PictorialInterpreta$onHorizontal($me)Reflec$on

t = 0

Posi$veTimeHalf-spaceRd+

= A⇥(A) =

⇥x

23May2016 Mul$pleReflec$ons

Reflec$onsonReflec$onPosi$vityWhatisRP?

An$linearIsomorphism

Reflec$onPosi$vityHypothesis

ConsequenceStability(Osterwalder-Schrader)

0 6 h⇥(A)A(t)i| {z }classical

= hA, e�tH AiH| {z }quantum

6 hA, AiH| {z }quantum

0 6 h⇥(A)Ai| {z }classical

= hA, AiH| {z }quantum


O-SAxioms≅WightmanAxioms

EnabledtheFirstNon-TrivialQFTModel

•  Weakly-coupledpolynomialscalarfieldsintwodimensions.Glimm,AJ,Spencer(1974)– Wightmanaxiomsforrela$vis$cQFT– Uniquevacuum– Massgap– Uppergap(isolatedone-par$clestate)


Mul$pleReflec$onBound


|hAi| 6 h⇥(A)Ai1/2

= |h(⇥(A))(t)A(t)i|1/2

…..h| {z }n boxes

i2�n

Pictorialupperbound:

h| {z }n boxes

i2�n

AlsoReflectVer$cally


…..

Pictorialupperbound:

…..

…..

Discretesymmetrybreaking

QuantumMechanics:UniqueNode-lessGroundState(Tunnelling)

FieldTheory:Non-UniqueGroundState(PossibleLackofTunnelling,asinIsingmodel)Dobrushin-Minlos:announcement1973

- +

Reflec$onsonReflec$onPosi$vityPhaseTransi$ons

•  Firstproofofphasetransi$onsinQFT.StronglycoupledGlimm,AJ,Spencer(1975)

•  Idea:useRPandmul$plereflec$onboundtoes$matedevia$onofmeanfieldfrom“Peierlsargument”studiedbyDobrushinandbyGriffiths.Therebyonecanshowthismethodalsoappliesinthefieldcase.

•  Dobrushin-Minlosretrac$on1976

•  Wightmanaxioms,uniquevacuum,massgapGJS1976



Con$nuousSymmetryBreaking

Fröhlich-Simon-Spencer(1976):Beau$ful“Infra-RedBound.”

d≥3,N≥1integrable


Fermions:Osterwalder-SchraderOsterwalder-Eckmann,BorthwickLawceGaugeTheory:Osterwalder-E.SeilerHigherSpin:OzkaynakComplexFields:AJ,Jäkel,Mar$nez Spectralcondi$ononatorus

Superspace:Osterwalder,(Lesniewski),AJ,inprogress

Reflec$onsonReflec$onPosi$vityOtherFieldTheories

SpinSystems:Fröhlich,Dyson,Israel,Simon,Lieb,Brydges,Sokal

Characteriza$onMajoranas:AJ-Pedrocchi,AJ-Janssens

Parafermions:AJ-PedrocchiAJ-Janssens

Reflec$onsonReflec$onPosi$vitySta$s$calMechanics

New:GeometricInterpreta$onofRP(workwithZhengweiLiu)

Ver$calReflec$on

= A


= A⇤

x

x

Asan$-isomorphism(planaralgebra).Theoperatoradjoint.

StringFourierTransform

(FsT )(x1, . . . , xn) = T (x2, . . . , xn, x1)


Par$alRota$on

23

Horizontal/Ver$calRela$on

hA⇤Ai > 0=

ParaisotopyRota$on+Horiz.-Reflec$on=Vert.-Reflec$on

=

TheoremConsiderascalar,fermion,orparafermionsta$s$calmechanicsinadoubledvonNeumannalgebra(e.g.pos./neg.$me).LetΘdenotetheTomitareflec$on.IfHisaHamiltonwithposi$veSFT,thenposi$vetemperaturestatessa$sfyRP.AJ-LiuPlanarparaalgebras(2016),arxiv1602.02662Usestwistedproduct:AJ-Pedrocchi,CMP337(2015),455–472AJ-Janssens,CMP(2016)hep://dx.doi.org/10.1007/s00220-015-2545-z. 23May2016 Mul$pleReflec$ons 24

IdeasconnecttoQuantumInforma$on(withZhengweiLiuandAlexWozniakowski)

•  Teleporta$on

18May2016 DIASSTPSPL 25

hep://arxiv.org/abs/1605.00127hep://arxiv.org/abs/1605.00321


State

SFT


=MaximallyEntangledResourceState

Fs|~0 i = |Maxi



ClassicTeleporta$onCircuitofCharlesBenneeet.al.

23May2016 30

AFurtherReflec$on

IstheRP-C*rela$onhelpfulforunderstandingRobert’sproofofRPinthecontextofReggecalculus?



AndNowSomePhotos!


RobertandJiminCargèse1979

9September1992,WhiteHartInn,Salisbury,CT 34

23May2016 AliceMackeyandRobertSeptember9,1992 35


CapriMay1993(PhilippeBlanchard)

37RobertwithShouchengZhang,hisformerdiplomastudentinthe1980’s

23May2016

AulaJune2002

38

23May2016 March19,2005atHarvard 39





Robert’sRe$rement16December2005

23May2016 44

19May2006Berlin,DürersMueer

Mul$pleReflec$ons 45

27February2009inBerlinbeforeconcertwithZehetmair&BerlinPhilharmonicconductedbyHeinzHolliger 46

23May2016 2006Berlin 47

23May2016

February28,2009BerlinPhilharmonicconductor’sroom

EdicsonRuizlessonfromHeinzHolligeron

“PreludioeFugafürSolokontrabass”

48

SchlossBrunegg,May14,2016

Skypecall,May232015

Kahlendamm3,Hannover50





23May2016

February5,2016Hamburg

55

IngridandherdaughterHaraldandhiswife

SomeQues$ons1  WhyisOsterwalder-Schraderposi$vitynota

centralfeatureinEVERYquantumphysicstextbook?

2  WhywasRobertnevera“full”professor?3  WhydidFUBnotregardRobertasoneof

theirmostdis$nguishedfacultymembers?4  Robert’sLastTheorem“Reflec$onposi$vity

insimplicialgravity”J.Phys.A,April2016doi:10.1088/1751-8113/49/21/215202


Hopefullysomeprogresswillbemade!

ManyThanks!!!


ETH


Documents

Mul$ple Reﬂec$ons, 23 May, 2016 · Life at Harvard in 1970’s • Robert led an unconven$onal life. • His friend Christa, whom he met on a skiing trip, was East German