愛因斯坦之夢理論物理基礎入門

1、Einsteinの夢,京都大學基礎物理學研究所小玉英雄,一般相対性理論,重力 ? 物質物質 ? 重力,黎明期?。保梗埃担保梗矗?1905 特殊相対性理論1915 一般相対性理論,1916 Schwarzschild解1917 Weyl理論1923 Birkhoffの定理1924 Eddington-Finkelstein座標1931 Chandrasekhar質量1932 中性子星の存在予言1933 Ho

2、rizonの概念(Lemaitre)1934 Tolman-Bondi解1939 一様星の重力崩壊,1917 靜的Einstein宇宙解 de Sitter解(Λ)1921 Friedmann解 (K)1932 Einstein-de Sitter解1934 Tolman解 (P)1935 Robertson-Walker計量,1929 Hubbleの法則（宇宙膨張）1933 Coma銀河団の

3、ダークマター,1900 輻射の量子論1905 光量子論,1921 Kaluza-Klein理論1925 Pauliの排他原理1926 波動力學1928 Dirac方程式1929 場の量子論　　　統(tǒng)一場の理論,,FRWモデルSchwarzschildブラックホール,発展期　１９４６－１９７４,1957 Regge-Wheeler方程式1962 Landau-Lifshitzの公式 Newman

4、-Penrose形式1963 Kerr解1965-70 特異點定理1967 靜的ＢＨの一意性1968 Ernst理論 Harrison変換1969 弱宇宙検閲仮説1970 Zerilli方程式1972 定常回転ＢＨの一意性 Teukolsky方程式1973 BHの面積増大定理 BHエントロピー1974 BHの蒸発,1948 くりこみ理論1958 拘束系の正準理

5、論1960 ADM形式1961 対稱性の自発的破れ1964 重力場のDirac量子化　　　クォークモデル　　　Higgs機構1967 Weinberg-Salam理論No-Go定理(Coleman-Mandula)1968 Veneziano振幅1973 QCD,1962 X線星の発見1963 QSOの発見1965 CMBの発見1967 電波Pulsarの発見1973—1978 CygX1が有力な

6、ブラックホール候補となる,1946 Big-Bang理論RW宇宙の線形摂動論1948 定常宇宙論1957 元素の起源1962 星の進化理論1967 WD方程式1968-70 Bianchi宇宙論1969 膨張宇宙における粒子生成1970’s 宇宙の熱史，銀河形成の研究,,Raychaudhuri方程式強エネルギー條件が満たされるとき，重力は引力となる．一旦収束し始めた非回転的光線束（時間的測地線束

7、）は　有限時間內に「一點」に収束する．,Hawking-Penroseの特異點定理 強エネルギー條件（＋一般性條件） 因果性條件 強重力條件（捕捉的集合の存在）の３つの條件が満たされるとき，無限に延長できない光的ないし時間的測地線が存在する,,（弱い）宇宙検閲仮説 [Penrose(1969)]靜的ブラックホールの一意性 [Israel(1967), Bunting-Masood-ul-Alam(1

8、987)]定?；剀灔芝楗氓郓`ルの一意性 [Hawking, Carter(1972), Mazur(1982), Chrusciel(1996)]?　重力崩壊の終狀態(tài)の予言可能性,重力崩壊により作られる特異點はホライズンに隠される．,漸近的に平坦で靜的な正則電磁真空ブラックホール解は（ホライズンが非縮退なら）球対稱で，Reissner-Nordtrom解に限られる ．,漸近的に平坦で定常な正則解析的電磁真空

9、ブラックホール解は（ホライズンが連結なら）軸対稱で，Kerr-Newman解に限られる．,転換期　１９７４－１９８９,1978 Baryogenesis1980’s 宇宙構造形成の組織的研究（摂動論、Ｎ體計算）1980 ゲージ不変摂動論1981 インフレーションモデル1982 新インフレーションモデル 量子ゆらぎからの構造形成 無からの宇宙創(chuàng)生1983 宇宙の無境界波動関數(shù) カオス的インフレーション

10、1988 Baby universe model,Wess-Zumonoモデル1975 No-Go定理(Haag-Lopuszanski-Sohnius)1978 D=11SUGRAモデル1980 Freund-Rubinコンパクト化1981 KK型超対稱統(tǒng)一理論の分析1984 超弦理論の誕生1985 Calabi-Yauコンパクト化1986 Ashtekar理論1988 ループ量子重力,1977 EPIによる

11、BH熱力學1979 正エネルギー定理 (Schoen & Yau)1980’s 解の変換論1982 荷電定常回転BHの一意性1983 正エネルギー定理 (Witten, Nester)1986 Myers-Perry解1987 靜的BHの一意性（PETの利用）,1970代後半—1980年代ダークマターの観測1988 CfA survey,1974 大統(tǒng)一理論,飛躍期？　１９９０－,199

12、5 雙対性による超弦理論の統(tǒng)合：M理論1996 Dブレイン、 F理論M理論の超対稱フラックスコンパクト化Horava-Witten理論1997 AdS/CFT予想1998 TeV重力理論2000 Landscape問題2002 フラックスコンパクト化によるモジュライ安定化,1993 位相検閲定理Gregory-Laflamme不安定1996 量子重力理論によるBHエントロピーの導出（SST/D, LG)2

13、001 ブラックリング解2002 高次元靜的BHの一意性2003 靜的高次元ブラックホールの摂動論,1992 COBEによるCMB非等方性の検出1994 連星パルサーPSR 1913+16の観測1998 現(xiàn)在の宇宙の加速膨張(IIa SNe)1999 BOOMERANG2003 WMAP 2005 Boomerang03インフレーションの確認，ダークエネルギー,1999 RSブレインワールドモデル2000

14、BWモデルの摂動論2003 KKLT構成 KKLMMTモデル,今後の課題,検証天體物理活動的天體（ブラックホールの物理）：　ジェット形成重力崩壊（數(shù)値相対論）重力波重力レンズ宇宙論宇宙進化モデル：　インフレーションモデルの確定観測的宇宙論：　ダークマターとダークエネルギー宇宙の初期條件と初期進化特異殘留物の物理數(shù)理厳密解の構成解の分類（ブラックホール）時空の大域的構造宇宙検閲仮説と時空特異點原理的諸問

15、題統(tǒng)一理論，量子重力理論,Higher-Dimensional Unification,Standard model ? (SO(10)) GUT: gauge-sector unificationhypercharge structure, αunification, neutrino massBaryon asymmetry, strong CP(Peccei-Quinn symmetry),Standard model

16、GUT,Ref: Wilczek, F: in Physics in the 21st Century, eds. K.Kikkawa et al.(1997, World Scientific),Coupling Constant Unification,Standard Model,MSSM,De Boer, W & Sander, C: PLB585, 276(2004)[hep-ph/0307049],Hi

17、gher-Dimensional Unification,Standard model ? (SO(10)) GUT: gauge-sector unificationhypercharge structure, αunification, neutrino massBaryon asymmetry, strong CP(Peccei-Quinn symmetry)GUT ? SGUT: boson-fermion co

18、rrespondenceDark matter, Λ problem, hierarchy problem，α unification,Supersymmetry,Super-Poincare algebraBoson ? Fermion : N=1 case:Positiviｔy of energy:Boson-fermion cancellation:(Massless) SupermultipletN=1:

19、N=2:N=8:,,Super-partners in SMSUSY breakingAdS-super algebra,Higher-Dimensional Unification,SGUT ? Sugra GUT: inclusion of gravityFlat inflaton potentialSugra GUT ? HD Sugra GUT: matter sector unifica

20、tionRepetition of families, Cabibbo/neutrino mixing, CP violationIncomplete (split) multiplets,Family Repetition,Standard ModelHigher-dimensional modelχのゼロモードの數(shù) ? familyの數(shù),Triplet-Doublet Splitting,Baryon nu

21、mber violation by HiggsOrbifold GUT (Kawamura model [2000])Ref: Nilles, H.P.: hep-th/0410160,Higher-Dimensional Unification,HD Sugra GUT ? Superstring/M theoryConsistency as a quantum theory, finite contro

22、l parametersNo Λ freedom (M-theory),Difficulties of SHD Theories,Choice of theoryM-theory or 10D superstring theoriesAmbiguity due to duality and branesCompactificationWhat determines the type of compacfication?Mo

23、duli stabilisationNo-Go theorem against accelerating expansionIdentification of our four-dimensional universeSUSY breakingMechanismControl,Moduli,Torus compactification:Effective action Cf. KKLT(Warped

24、 compactification with flux), Landscape problem,We have to find a compactification in which all moduli are stabilised at high energy scales, except for inflaton, and allows for supersymmetric inflation.,No-Go The

25、orem,ProofFor the geometryfrom the relationfor any time-like unit vector V on X, we obtainHence, if Y is a compact manifold without boundary, is a smooth function on Y, and the strong energy conditi

26、on is satisfiedin the (n+4)-dimensional theory, then the strong energy condition is satisfied on X.,For any (warped) compactification with a compact closed internal space, if

27、the strong energy condition holds in the full theory and all moduli are stabilized, no stationary accelerating expansion of the four-dimensional spacetime is allowed.,Summary,General relativity has played a leading role

28、in cosmology and astrophysics in these 90 years and produced new predictions, often by interplays with developments in microscopic physics. Many of them, although regarded as exotic at first, have been successfully confi

29、rmed by observations. Now, however, we are experiencing a new situation in which observations precede theoretical predictions. In particular, the Dark Energy/Cosmological Constant problem is clearly beyond the scope of

30、general relativity and can be resolved only by a unified theory of matter and gravity.Recent experimental and theoretical analyses of the standard model for elementary particles as well as cosmological models also stro

31、ngly suggest that the matter sector and the gravity sector should be unified, and it is highly likely that the unified theory is higher-dimensional.,,At present, we have a very strong candidate for a unified theory, i.e

32、. superstring/M-theory. However, it is still far from complete. Furthermore, there are serious obstacles in constructing a realistic universe model and low energy physics in term of them, such as the moduli stabilisation

33、 problem, no-go theorem against accelerating expansion of the universe and the SUSY-breaking mechanism problem. In addition to applications to cosmology and astrophysics, a huge amount of investigations have been done c

34、oncerning mathematical aspects of general relativity. Thereby, various fascinating results such as singularity theorems, black hole uniqueness theorems and positive energy theorems have been obtained. Although they hav

35、e not produced any observable new prediction up to this point, they have provoked various new theoretical developments such as black hole thermodynamics and the cosmic censorship problem. In higher-dimensional unified t

36、heory, such mathematical investigations become richer and will have a crucial importance in getting observable predictions.,,From the history of the last century, we have learned that timeliness is crucial for successful

37、 investigations. Now, it is time for you to bet on whetherSpacetime is really higher dimensional microscopically,OrSpacetime is four-dimensional, and the apparent higher-dimensionality of a unified theory is just of a