2016.04.16「岩崎洋一先生７５歳記念祝賀会」(2016/4/16) スライド

５０年間の研究生活を振り返ってみなさまに感謝をこめて

岩崎洋一
1

研究生活

50年間：1965 – 2016

phase I

1965&&&&&&&修士２年&

船出

1969&'1975

phase&II

1972-1974 City College at New York1975
筑波大学講師

模索

京都大学基礎物理学研究所

助手

1977 – 1978 Institute for Advanced Studies at Princeton
1981&'&&&&&&&&&&&&&&&格子QCDの研究&

phase&III
発展・成熟

1983&'&&&&&&&&&&&&&&&RG&improved&ac>on&
1987'&1991& QCDPAX&project&&
1992–&1997& CP'PACS&project&phase&IV
黒の時代

1998–&2009& 大学行政

phase&V
復活

2011- 2016

復活（研究活動）2

Phase I

船出

大学院時代から助手まで

3

Episode 1
湯川秀樹先生の逆鱗に触れる1965 修士２年

日本大学（お茶の水）研究会
素粒子の剛体モデル
鮮烈な全国デビュー？！

スピン

半整数はあり得るか？

講義

量子力学：軌道角運動量とスピン
L2 Zlm = l(l + 1) Zlm

通常の議論

１価性から

Lz Zlm = m Zlm
L+ Zlm = cZlm+1
L Zlm = cZlm 1

m = 0, ±1, ±2, · · ·???

スピノールのときは２価性が許されるのに、なぜ???

Zlm (✓ ) = ⇥(✓)lmm()) = exp(im )L2 Z1/2,1/2 = 1/2(1/2 + 1)Z1/2,1/2

l = 1/2 とする

L2 Z1/2, 1/2 = 1/2(1/2 + 1)Z1/2, 1/2

L+ Z1/2,1/2 = 0⇥1/2,1/2 (✓) = sin

m(

条件&A

1/2

✓

Z1/2, 1/2 = L Z1/2,1/2
cos ✓⇥1/2, 1/2 (✓) =sin1/2 ✓Lz Z1/2,1/2 = 1/2Z1/2,1/2
Lz Z1/2, 1/2 =1/2Z1/2, 1/2
L+
Z1/2,1/2

Z1/2, 1/2
L

条件Aを満たす表現になっているか？？？ 5

表現になっているか？

⇥1/2,1/2 (✓) = sin1/2 ✓⇥1/2, 1/2 (✓) =cos ✓sin1/2 ✓エルミート表現になっていない（無限次元表現）
L Z1/2, 1/2 6= 0
Pauli の量子力学の教科書：47ページ
A general criterion for the admissibility of eigenfunctions, which does not from the beginning assume theirsingle-valuedness, has been given by W. Pauli.5* This criterion states that repeated action of the operators
corresponding to physical quantities on the eigenfunctions should not lead outside of the domain of square
integrable eigenfunctions.

5): Pauli の1939 年のドイツ語の論文

6Episode 2
1968 - 69 東大安田講堂 脇 テント村

素粒子研
安田講堂脇

同学年

山本義隆

テント村

K、M、A 教授

夕方

全共闘議長

荒船、岸本、・・・
訪問

これ以降の生き方に影響京都大学基礎物理学研究所

助手

着任&Fukuda&,&&,Sasaki&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&Kawabata,&&&&&&&&&&&&&&&&,&Konuma,&Kawasaki,&Maki,&&Yukawa,&Ida,&Sato,&Muta,&Iwasaki

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&Ida,&&Yukawa,&Maki,&Matsuda,&Konuma,&Horiu>,&Iwasaki&
kitakado,&&&,&Tamagaki,&Kawarabayashi

9Episode 31971 量子重力 one-loop
当時、水星の近日点移動 の観測結果 は アインシュタイン理論 から8 % ずれていた
水星の近日点移動はポスト・ニュートニアン・ポテンシャルの大きさによる
P2kmM
k2 m M 2
H=
3 2 2
2m
r
c r
また、当時、古典的重力現象は平面グラフだけによると間違って信じられていた

Feynman: Acta Polonica (1963) などにもそう書かれていた

具体的に計算してアインシュタイン理論と同じ結果を得たという論文も存在
そこで、４次のグラフからポスト・ニュートニアン・ポテンシャルを導き、
アインシュタイン理論と同じ結果になることを確かめた
Prog. Theor. Phys. 46 (1971)1587

重力粒子は２階のテンソル＝＞複雑な計算

1587

Progress of Theoretical Physics, Vol. 46, No. 5, November 1971

Quantum Theory of Gravitation vs. Classical Theory*)--Fourth-Order Potential-Y oichi IWASAKI

Research Institute for Fundamental Physics, Kyoto University, Kyoto
1594

Y. Iwasaki(Received May
18, 1971)§ 1.

Introduction
Downloaded from http://ptp.ox

In constructing a quantum theory of gravitation there are two main problems:
One is to formulate it consistently and the other is to describe gravitational phenomena correctly by it.
ge
The former includes, for example, f maintaining
unitarity,
Lorentz invariance
Fig. 1. Some of the fourth-order diagrams. The wavy line represents the graviton and the solidand gaugelineinvariance,
and the removal of divergences. In the covariant formamatter.
lism1)'2),S) which we use in this paper this problem has been resolved except for

Downloaded from http://ptp.oxfordjournals.org/ by guest on March

The perihelion-motion of Mercury depends on the fourth-order potential in quantum field
theory; it is a "Lamb shift ". In spite of the unrenormalizability of the theory, we haveextracted a finite and physically meaningful quantity, a fourth-order potential, from fourthorder graphs. We have also discussed briefly renormalization of the Newtonian potential in
the fourth-order perturbation.
The Hamiltonian obtained is the same as the classical one and so it cannot explain the
Dicke-Goldenberg experiment.
acd
We have calculated
fourth-order bpotential also in Q.E.D.

論文の優先権の微妙さ
1977年プリンストン高等研究所で、Wilczek と Zee とお茶を飲んでいる時に４次の計算
はどのくらい大変だったかと聞かれ、さらにBoulware 等の論文の存在を教えてくれた
PTPの論文より４年遅れての論文で、４次の具体的な計算はしてなく、PTP を脚注で引用しているだけ

著者からは何の correspondence なし

たちの論文を引用しがち
ANNALSOF PHYSICSClassical

引用も２番目の論文では自分

89, 193-240 (1975)

GeneralRelativity

Derivedfrom

Quantum

Gravity*

DAVID G. BOULWARE
Physics

Department,

Universityof Washington,

Seattle,Washington

98195

Massachusetts

02154

AND
S. DESER
Physics

Department,

Brandeis

University,

Waltham,ReceivedJuly 18,1974

The existence of long range macroscopic attractive forces between masses implies
the existence of a mediating helicity k2 particle in special relativistic quantum particle
theory. It is shown that this fact alone, without assuming the existence of an underlying tensor field, uniquely determines the long wavelength structure of quantum
gravitation to be that of Einstein’s theory. This equivalence is shown by deriving, fromthe Ward identities associated with the graviton propagator, the tree graph structureof the graviton-graviton
and graviton-matterinteraction and establishing that the12

Phase 2

模索

1973 -- 78 研究目標、方法の模索
1973 ~ 74 素粒子物理学

革命期

13

Episode 4 -1
京都

東京

名古屋

研究風土の違い1969 基礎物理学研究所
理学部

湯川秀樹博士

所長

小林、益川

東京

S行列

ハミルトニアン不必要？

京都

広がりのある素粒子場の理論の拡張？

かっての N. Bohr ??
名古屋

徹底した場の理論の適用と模型構築
かっての H. Yukawa ??

京都

東京

名古屋

セミナーでの質疑応答&
論文作成

九後さん

研究風土の違い

たまの息抜き小林誠宅Couyhng of the trace of the energy-momentum

Episode 5
Department

1977

Y. Ivmsaki
of Tsukuba, Ibaraki, 300-31, Japan(Received 29 September l975}

of Physics,

Trace Anomaly

tensor to two photo

University

間奏曲%e derive a theorem on the coupling of the trace of the energy-momentum

tensor to two photons,

Coupling&of&the&Trace&of&the&Energy'Momentum&Tensor&to&Two&Photons&
tra" e of the energy-momentum t
The purpose of this paper is to derive a theoremon the coupling of the trace of the energy-moPhys.&Rev.&D15(1977)1172
8„=mpp+ (gn —l)Z, (8~A —8
mentum tensor to two photons. 'Theorem.

Consider the vertex(0Ie„„(0)Iy(~„k,), y(~„k,))=(e, ~, k, k, —c, k, e, k, )E(q'). (l)Here 8„„is the trace of the energy-momentum
tensor, 8„„, and q = k, + k, . Then

E(0) =0.

Proof. The most general form of the vertex&oI.

8. (0} Iy(~„k,), y(~„k, »Adler&et&al.&&Phys.&Rev.&D15(1977)&1721&
ls given bytrace&anomaly

i E,',E'„(k, —k, ) „(k, —k, ) „B(q'}Adler&“Anomalies&to&All&orders”&+ ,'(E', E2~+—F„',F28)(k, +k, ) (k, +k, )~C(q') .
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&arXiv:hep'th/0405040
Here E,*,= (k, ) „(e,), —(k, ),(e, ) (i = I, 2). To de»vee„, =mg(+ g M, g, g, ,depending on the methods of theEquation (7) corresponds to theregula. rization, ' while Eq. (8) co
Pauli-Villars regularization. ' I
the dimension of the space-timeand M,. represent the fields andauxiliary fields. We may consid
Eqs. (7) and (8) as the renormaliz
we calculate the matrix element
To obtain the matrix element
mentum tensor, we should keep,
calculation, the finiteness of theand the conservation law of thetensor. To keep the finiteness w

auxiliary fields (the regulators}
Villars method, while we16 continu

elementof theenergy-momentum
defined insimilar andway with
by Pauli-Villars
with ...
denoting
terms
that vanish bytensor,
the equationsof amotion,
N [Fλσ F λσ ]regularization,
specifiedby the conditions that its zero momentum transfer matrix elements beAdler&が論文のレフェリーであり、&IAS&に１年間滞在の招待状をだした???&m0
m0 and a two photon
tween two electronstates,vacuumare⟨0|θµµ |γγ⟩
−and⟨0|θµµbetween|γγ⟩M0 = them0 ⟨0|j|γγ⟩− M0 ⟨0|j|γγ⟩M0 , state,(21)
given by the corresponding tree approximation matrix elements of the operator
私は1976年の秋、応募書類をいくつかの研究機関に出した。&
imposition of gauge invariance (to elimiwith λσ
j = ψψ the scalar current. With theµZ3−1 Fnate. Taking
matrixelementsofθ
betweenelectronstatesat zerothe
momenλσ F quadraticµ side of thisdivergences), the left handequation
approaches
regu12月の中旬に&IAS&とCERN&から招待状を受け取った???
tum transfer
then
gives
the
condition
larized trace of the energy-momentum tensor, and the first term on the right is well 1
defined and gives the matrix element of the naive trace. However, for the scalar cur=m.
(23)
K1 ⟨e(p)|m0 ψψ|e(p)⟩rent, gauge invariance combinedwithdimensional
analysis shows that for large M0 ,ANOMALIESTOALL
ORDERS−1
ρσ0
we have⟨0|j|γγ⟩Musing∝ MtheFρσ |γγ⟩M0 , andso the forsecondon theright
0 ⟨0|F
However,an analysis
Callan-Symanzik
equation
the term
electronpropagaapproaches a nonzero limit as M0 → ∞, and gives the trace anomaly. Pursuing the
tor shows that
Stephen L. Adler
details by computing the proportionality constants, one sees that Eqs. (20,21) give
Institutefor Advanced
mStudythe correct anomaly coeﬃcientsin thetwoThis , way of deriving the trace⟨e(p)|mDrive,(24)= cases.
0 ψψ|e(p)⟩EinsteinPrinceton,
NJ
08540
USA
1 + δ(α)
anomaly shows clearly that it is a scalar analog
of the pseudoscalar axial-vector
E-mail: adler@ias.edu
anomaly, a fact that will figure in the discussion of anomalies in supersymmetricwith 1 + δ(α) = (m/m0 )∂m0 /∂m, so that K1 is given by K1 = 1 + δ(α). Now taking
theories.
the vacuum
to two photon
matrixanomalies
elementbeganof θµµroughly
at zerofive
momentumtransfer,andMy aninvolvement
years
later,
PhysI giveaccount ofwith
my trace
involvement withthe chiral anomaly,
andwithwhen
the nonλσ
using ical
Iwasaki’sandthecondition
for
Nthe
[F
F orders], we calculation
get a noted
secondrenormalization
theoremfor defining
thea chiralanomaly
andall
Review theorem
sent meforrefereeingpaper
byIwasaki[54].
Inλσthis
paper,
which
conditionof relevancethe trace toanomaly,
as well as
relatedwork abyothers. theorem
I then briefly
thetrace anomalies,
Iwasakiprovedkinematicon thediscussvacuumimplicationsof
these
resultsformorerecentdevelopments
inanomalies
into two photon matrix element of the trace of the energy-momentum tensor,superthat is0=[1+
δ(α)]⟨0|m
ψψ|γ(p)γ(−p)⟩
symmetric
theories.
0
an analog of the Sutherland-Veltman theorem for the vacuum to two photon matrix−1+ K2 ⟨0|Z
Fλσ F λσ |γ(p)γ(−p)⟩(25)
element of the divergenceof thecurrent. Just
tree as. the latter has a kine3 axial-vector
2matic zero at q = 0, Iwasaki showed that the kinematic structure of the vacuum to
1. Introduction
However,analysisof theelement
Callan-Symanzik
equation for tensor
the photon
propagatorshows
two photon
matrixof the energy-momentum
implies,when one takes
that
A distinguishingfeatureof thechiral andtrace
in gauge
theoryis thatthe trace, that there
is alsoa kinematiczero
at q 2anomalies= 0, irrespectiveof thepresenceof anomalies(justthedetermined
Sutherland-Veltman
resultin the presenceof anomatheircoeﬃcients
canasbeto all orders
perturbation
theory.
My aimsβ(α)
1 ofholds⟨0|m=route−0 ψψ|γ(p)γ(−p)⟩lies). article
Readingare
thissuggested
the ideathat leading
just as the Sutherland-Veltman
in thistoarticle
surveythe historical
4 1 + δ(α) to the discovery of thistheorembe used andas partof an argument
to provethepropertyof cananomalies,
to reviewits current
status.nonrenormalization
In the first part Iofdiscuss

×⟨0|Z3−1 Fλσ F λσ |γ(p)γ(−p)⟩tree ,(26)
the nonrenormalization of thechiral anomaly, in its historical context and thenfrom a modern perspective. In the second part I discuss the closely analogous resultsh In addition to writing a favorable report on Iwasaki’s paper, I invited him to spend a year at thelinking the coeﬃcient of the trace anomaly to the renormalization group β function.
Institute for Advanced Study, which he did during the 1977-78 academic year.
In the third part, I conclude by discussing the interplay of these two results in thecontext of supersymmetric theories.

17

Episode 4 - 2
1977--78 Institute for advanced study at Princeton
Callen,&Dashen,&Gross&& &
&
&
&
&
&
&
Wilczek,&ZeeInstanton&gas&&what&ﬁx&the&scale&of&strong&interac>on&?&

非摂動効果の重要性&
特にトポロジカル配位の重要性&
理論が非摂動的に定義されていること

格子QCD

K. Wilson: lattice gauge theories

Phase&III

発展・成熟

格子QCDをターゲットにしてその全貌を明らかにする19

ターゲット：格子QCD
構成的場の理論&&&定義できるか

連続極限
RG&'>&phase&diagram;&ﬁxed&points;&RT

RG&improved&gauge&ac>on
格子上のクォーク&Wilson&quark&
Staggered&quark&&
Chiral&quark

２つの主要なテーマ

staggered&quark
det&D&^{1/4}&??????
Wilson&quarkchiral&symmetry&とクォークの質量20Episode 6
RG improved gauge action (n parameters)
繰り込み群の RT に近いという条件 => (n-1) パラメーター空間
インスタントンの安定性と不安定性の境界 ＝＞ (n-1) パラメーター空間
２つの空間同じになる

E ' 8⇡ 2 |Q|

n=1でも充分スケーリングを改善

submitted to Nucl. Phys. B
comment by referee
Reply by YI
comment by referee
Reply by YI

1. already done by Symanzik
2. different from Symanzik
3. then should be wrong
4. it really improve the scaling

Repeat the cycle above !
このプロセスを２年間繰り返した。その間、improvement を実証することに21

CTP-TAMU-06/93
conference to reveal to an unsuspecting world his
result [12] that black holes

evaporate! Ironically, Christensen and Fulling [13] were subsequently to show

arXiv:hep-th/9308075v1 16 Aug 1993

Twenty Years of the Weyl Anomaly †that in two spacetime dimensions the Hawking eﬀect is due entirely to the‡trace anomaly. Two dimensionalholes, and the eﬀects of the Weyl
M. J. Duﬀblack

anomaly in particularCenter[14, 15,16], are currently
enjoying a revival of interest.
for Theoretical
Physics2

Physics Department
Texas A & M University
College Station, Texas 77843

Anomaly? What anomaly?

物理学研究者が新しいアイディアを受け入れるにはSome cynic once said that inABSTRACT
order for physicists to accept a new idea, they
In 1973
twothroughSalam protégés(Derek Capper
and stages:
the author) discovered
must firstpass
the following
threethat the conformal invariance under Weyl rescalings of the metric tensorgµν (x) → Ω2 (x)gµν (x) displayed by classical massless field systems in interac(1)It’s wrong
tion with gravity no longer survives in the quantum theory. Since then these
Weyl anomalies have found a variety of applications in black hole physics,
３つの段階を必ず経る(2)
It’s trivial
cosmology,
string theory and statistical mechanics.
We give a nostalgic review.

(3) I thought of it first.

In the case of the Weyl anomaly, however, our experience was that (1)and (2) got interchanged. Being in Oxford, one of the first people we tried toimpress with our new anomaly was J. C. Taylor who merely remarked “Isn’t
物理学研究者（集団）は保守的な面も持っている
CTP/TAMU-06/93
1993 obvious?”.
that Julyrather†In a sense, of course, he was absolutely right. He

Talk given at the Salamfest, ICTP, Trieste, March 1993.

22

Many evidences for improved scaling
SU(5) gauge theory
Nf=2 QCD at finite temperature
behavior of Kc and Kt
O(4) or O(4)xO(2) scaling
Nf=3
Disapearance&of&kinks&or&peculiar&behavior&observed&with&the&one'plaquene&&ac>on&and/or&
the&Symanzik&ac>onearly scaling is more important than power of O(a)Transition between different topological sectors<= RG improved action
Now called the Iwasaki action

23

Episodes 7 and 8
自前のスパコンを製作

QCDPAX and CP-PACS
プロジェクトの背景
非摂動的計算 計算物理が有効&
当時のスパコン 性能不足&
格子QCD

並列計算機に適している&&&&メーカーの製品なし&

筑波大 星野力 原子炉シミュレーションのため、小型並列計算機製作&
岩崎、小柳の仲介により 星野と会う
４５歳の決断（山手線）：QCDPAX&プロジェクト代表者になる&
QCDPAX&に引き続き、CP'PACS&プロジェクトも採択された
24

プロジェクト推進の基本的考え
研究者は、ガリレオの時代から最近の重力波観測装置に至るまで、&最先端の実験装置・観測装置を開発することにより科学の最先端を切り開いてきた。&
スパコンは実験装置であり、観測装置である。

プロジェクト遂行の要
人（個性を尊重する、ユニークさは分野ごとに異なる）&
人の和（特に理学と工学）&
場（人の和の実現）&
組織（場を提供）

共同研究プロジェクトの鍵
理学・工学それぞれのゴールを設定し、両方実現
工学 世界一の計算機を開発
理学 世界最先端の物理結果を得る

25

具体的経験QCDPAX
代表者 岩崎、星野&
人数 ５ー７&
予算 ３億円（特別推進）&
場：&&&&&pre'internet&

メーカー アンリツ&
ハード ネットワーク柔軟性欠ける&
ソフト

アセンブラ＋func>on&呼び出し&
金谷、吉江&

性能

15Gﬂops&&

物理

ハドロンスペクトラム&
SU(3)&ゲージ理論相転移

CP'PACS
代表者
人数
予算

岩崎、宇川、中澤&
20&'&30&
22億円(CP'PACS)&&&&&&&&&&&&&&&&&&&約60億円(センター新設費用)&
場
センター&
組織
計算物理学研究センター&
メーカー 日立製作所&
性能&世界スパコン500&一位&

物理

世界の最先端の結果&
別記

センター関係経費：&
概算要求
休暇

１日/５年
26

CP'PACS&記念誌
https://www.ccs.tsukuba.ac.jp/ccs_introduction
読み物：新幹線やソファーで気楽にQCDPAX&の前でボードを持って

日経ビジネス28

Polyakov&loops&複素平面でのヒストグラム分布

相転移点上SU(3)&ゲージ理論
conﬁned&phase&の原点のピークとdeconﬁned&phase&の&Z(3)&対称なピーク
QCDPAX

0.15

-0.15

0.15

0

-0.15

0

Re !

Im !

K.&Kanaya&et.&al&(1992)
29

Complete&of&the&computer&building&1993
計算機棟

CP-PACS 用

Complete&of&the&research&building&1996

Members&of&the&collabora>on&in&front&of&
the&CP'PACS&computer&1996

Shutdown&of&the&CP'PACS&computer&2005

TFLOPS

Development of Computers
10

1
Parallel Computers

GFLOPS

100

10Vector Computers

1

0.1
1975

1980

1985

1990

Year

1995

2000

2005

CRAY
CDC/ETA
HitachiFujitsu
NEC
IBM
TMC
nCUBE
intel
Fujitsu AP/VPP
CRAY
IBM
CP-PACSQCDPAX
Columbia
APE
GF11(IBM)
FNAL
UKQCD
NWT

CP-PACS 物理結果

35

0.4

# =5.85

0.4

0.2

0.2

+

*

0,0 " ~ / - ~ - ' - - --". . . . .

*mqe(m~o) 2
0.5 . . . . . . . . .
, . . . . . . . . .
2.5
mqe
a
0.5 . . . . . . . . .
, . . . . . . . . .
0.4 ~ = 5.65
2.0
Nt =4 a0.4 ~ = 5.65
0.3
" : ( m , a ) 2 Nt =4~ . j t ~ 1.5~ ~Quark Mass

K : 0.16169,+~, . . . . ; . . . . . .

0,0 " ~ / - ~ - ' - - ~:ing masses at finite t e m p e r a t u r e . Fig. 3 shows the re-.......................

o.1

~:

Episode 7.......................

o.1

K?u"rk(T> Tc)~K~uark(T<T,:)~K'~(T<Tc) . ( 6 )T h e r e f o r e we m a y s i m p l y call t h e m all Kc.
N o w letT hus
the t hp ei omn all
screene r ediscussf o r e wethem aresultsy s i m p lfor
y callKc.
ing masses at
e mdiscussp e r a t u r ethe
. Fig.
3 shows
the preN ofinite
w let tus
results
for thei o n screen-# =5.85,~, . . . . ; . . . . . .

"-----

K : 0.16169-". . . . .

"-----

definition of quark mass
- 0 . 2 non-trivial since theK =quark
0.17200 1is confined

0.3":(m,a)2~ . j t ~ -(m~o) 2
2.5
2.0
1.5

/

- 0 .I2. . . . I . . . . I . . . . I , , s , l , , , , I
KI,,I= 0.17200 1....
I ....
0
~
2
3
4
5
6
7
8
/
--0,~
,I
....
....
I ....
I,,I
qI . . . . IZ. . . . I . . . . I , , s , l , , , , I
0
~
2
3
4
5
6
7
8 O0 ~
Fig. 1. Typical results for R(z)/G,,(z) whichZtends to 2mq for
--0,~

,I

....

M. Bochicchio et al. NP B262(1985)
S. Itoh, et al. NP B274(1986) 0.0m ( AW I

large z. The data are at fl= 5.85 on the N,=4 lattice. The hopping
O0 ~0.0~ . . . . .
0.5
Fig. 1. Typical results for R(z)/G,,(z) which tends to 2mq for . . . . . . . . . . . .
parameter where m~ vanishes on the N,=8 lattice is 0.16169.
- 015.5
6'0
615
7.0
7.5
large z. The data are at fl= 5.85 on the N,=4 lattice. The hopping
Note that 2mq is consistent with zeroqat this hopping parameter.
. . . . . I ./ K . . . . . .
~ . . . . .
0.5
q parameter where m~ vanishes on the N,=8 lattice is 0.16169.
- 015.5
6'0
615
7.0
7.5
Note that 2mq is consistent with zero at this hopping parameter.
(m~r0)2
mqo
I/K

Y. Iwasaki et al. PLB220(1989)

m (confined)= m (deconfined)

0.5

rnq0
0.5 . . . . .
. . . . . . . . . . . . . .
rnq0
Quark
0.5 mass. . vs.
. . 1/K.
. . . . . . . . . . . . . .
0.4# : 5.85 Quark mass vs. 1/K
05. : 0.4
NI =4 # : 5.85
0.2

• :0 5NI =. : NI =40.2• : NI =
~r

0.1

0.0 ,

I

,

i

,

,

I

-

i

0.1

,

~

- I

-

-

- i

i

i

i

-

-

1.5

0.3
• : (mTr0)2
•

0.0

~r
-

, ~

[ , . ~ ~ /

2.0

0.4

0.3

[ , . ~ ~ /

,

0.1

0.0
-0.1
55 '

,

0.4

0.2

2.5

mqo
0.5

:

0.2

l ~ / {

rnq0

• : (mTr0)2

7r

0.1

•

:

rnq0

,

7r

1.0

(m~r0)2
2.5
2.0
1.5

l ~ / { 0.5

1.0

0.0

0.5

,

, ~ , , 0.0
, ~ ,
~ ,
,
,
,
~ . . . .
~ ....
-0.5
-0.1
6.5
7.O
7.5
5.5
6.0
, ~, , , ~ ,
~ 1/K
,
,
,
,
~ . . . .
~ ....
-0.1
6.5
7.O
5.5
6.0
i
Fig. 3. (a) Quark masses and pion screening
1/Kmasses at//=5.65
7.5

0.0

-0.5
6.5
7.0
7.5
7.5
, ~
,
I
,
i
,
,
I
i
,
~
I
i
i
i
I/K
-0.1
55 '
6.0
6.5
7.0
on the N,=4 lattice. The arrow marks the hopping parameter
Fig. 2. The results for the quark masses at //=5.85. The arrow
I/K
Fig. 3. (a)massesand(b)
pion
screeningwhere m~, vanishes
on Quark
the N,=8
lattice.
Thesame as massesin (a) at//=5.65
marks the hopping parameter where m~ vanishes on the N t = 8
on
the
N,=4
lattice.
The
arrow
marks
the
hopping
parameter
Fig.
2.
The
results
for
the
quark
massesat//=5.85.
The
arrow
except for//=5.85.
lattice. The straight line is the fit to the data on the N , = 4 lattice.
6.0

mu&?&md&?&ms&?&36

クォーク u,dの質量 mud = (mu + md )/2
黒：Nf=2

白抜き: Nf=0: クエンチ近似
AWI
VWI

Axial Ward Identity
Vecor Ward Identity2
Nf = 0AWI とVWI 連続極限で一致 Nf =&&&&&&&&&と&&&&&&&&&&&&&&&&異なる
mud =4.47(16) MeV (Nf=0)

mud =3.45(20) MeV (Nf=2)

mud(µ=2GeV) [MeV]

5.0
VWI
VWI,PQAWIVWI, qStd
AWI, qStd
VWI, qImp
AWI, qImp

4.0

3.0

2.0

0.0

0.5

−1

1.0

1.5

a [GeV ]37

s クォークの質量 ms
140

190

VWI
VWI,PQAWIVWI, qStd
AWI, qStd
VWI, qImp
AWI, qImp

120
110
100
90

150
130
110
90

80
70

VWI
VWI,PQAWIVWI, qStd
AWI, qStd
VWI, qImp
AWI, qImp

170ms(µ=2GeV) [MeV]

ms(µ=2GeV) [MeV]130

φ input

K input
70

0.0

0.5

−1

1.0

1.5

0.0

0.5

mK &input

ms=89(6) MeV

m

Nf=2

ms =111(4) MeV Nf=0

−1

1.0

1.5

a [GeV ]a [GeV ]一致
15-20 % ずれ

input

ms=90(10) MeV Nf=2
ms=132(5) MeV Nf=038

ハドロン・スペクトラム
full&2+1&QCD&spectrum&by&PACS'CS

39

物理結果
ハドロン質量ハドロン崩壊定数

実験値と一致
実験値と一致クォーク質量mud 連続極限でVWI とAWI と一致
ms 連続極限でVWI とAWI と一致; mK input とm

input 一致格子QCD 構成的基礎理論として確立
予言能力
有限温度での相転移、クォーク・グルオン状態の解明
重いクォーク物理
原子核物理

1997
Lattice Conference
Edinburgh
ネス湖

1987
Lattice Conference
Capri
ローマ
41

バーベキュー&at&宇川邸

42

Episode 10

2011- 2016 復活（研究活動）
1987'&1991&

QCDPAX&project&&

1992–&1997& CP'PACS&project
1998–&2009& 大学行政

黒の時代

人生の幅が広がった経験したことのなかった幅広い世界を垣間み幅広い分野の人と接することができた

大学運営も研究プロジェクトも、人間の信頼関係が基本
大学運営において様々なことを経験

宇川さん：学長特別補佐（情報関係）

2011.3.11 東日本大震災
物理研究活動引退を決意

2011.10.24-26 KMI Inauguration Conference
物理への興味 再度、火がつく

IAB
43

Conformal theories in SU(3) gauge theories
黒の時代直前 2004 年からの続き

propagators with Yukawa-type decay ?
柳田 さん => 中山さん
New idea : Conformal theory with an IR cutoff

large Nf⇤
Conformal window Nf  Nf  16

Nf⇤ = 7

RG scaling relation
IR fixed point in the deconfining phase of QCD (unexpected)(1) It’s wrong(2) It’s trivial(3) ???
Property of Quarks and Gluons to be clarified

Phys Rev.D87(2013) 071503
Phys.Rev. D89 (2014) 114503
Phys.Lett.B 748 (2015) 289

with K. Ishikawa, Yu Nakayama and T. Yoshie

44皆様のおかげで、
５０年間の楽しい研究生活を送ることが出来ました
共同研究、議論、批判など
有り難うございました

家族には迷惑をかけっぱなしで申し訳なく、また心から感謝しています。
45

５０年間の内に、家族は1人が２人になり、４人になり、今は１０人になりました。
研究も家庭も若い人に未来を託したい。

46

ご清聴有り難うございました

47