重力と宇宙 新しい時空の量子論
|
|
|
- さいぞう ふじつぐ
- 5 years ago
- Views:
Transcription
1 Summer Institute at Fujiyoshida, 2009/08/06 KEK/ Conformal Field Theory on R x S^3 from Quantized Gravity, arxiv: [hep-th]. Renormalizable 4D Quantum Gravity as A Perturbed Theory from CFT, arxiv: [hep-th]. From CFT Spectra to CMB Multipoles in Quantum Gravity Cosmology, arxiv: [astro-ph] with S. Horata and T. Yukawa.
2 1. 2. CFT
3
4 Einstein gravity On-shell renormalization Einstein gravity N=8 supergravity? [! ] Wilson Superstring theory 10 4
5 Higher-derivative quantum gravity power-counting renormalizable ghost mode Lee-Wick-Tomboulis approach Horava approach CFT approach Regge DT (dynamical triangulation) Regge Einstein DT CFT approach 5
6 Lee-Wick-Tomboulis approach : resummed propagator Horava approach : Ghost IR ) Lorentz ghost CFT approach (our model) : (CFT) ghost mode 6
7 CFT approach 60 Einstein 70 (Lee-Wick) ( ) Hathrell Polyakov 4 Riegert 00 Riegert (Wheeler-DeWitt = conformal algebra) 7
8 CFT Conformal Field Theory on R x S^3 from Quantized Gravity, arxiv: [hep-th]
9 Einstein BH) Compton Schwarzshild BH Einstein 9
10 CFT 10
11 The Action (Weyl + Euler + Einstein) conformally invariant (no R^2) Planck constant 11
12 Wess-Zumino Conformal variation of effective action (=path integral by conf. mode) bare action (conf. anomaly) Integrability condition Weyl action and Euler combination (no R^2) 12
13 t (conformally flat) Riemann cf. gauge theory: Einstein 13
14 Jacobian = Wess-Zumino (Conformal Field Theory) ( ) : 14
15 (diffeomorphism inv.) : gauge parameter Mode decomposition traceless no coupling const. coupling const. Conformal mode and traceless mode are decoupled! 15
16 t = 0 Weyl cf. 16
17 t = 0 ( ) conformal Killing vector Traceless tensor mode! Conformal symmetry (on ) Other fields: fixed by physical state condition = Wheeler-DeWitt equation to remove conformal-mode dependence 17
18 For example by conformal Killing vectors on flat background Weyl 18
19 CFT This model : CFT + perturbations ( ) cf. 4 Free + perturbations graviton picture 19
20 WZ Euler 2 4 Euler WZ Liouville Riegert 20
21 Renormalizable 4D Quantum Gravity as A Perturbed Theory from CFT, arxiv: [hep-th]
22 Dimensional regularization all orders, diffeomorphism invariant 4 D cf. DeWitt-Schwinger method one-loop order conformal anomaly heat kernel 22
23 D D dimensional integrability bare action Euclidean sign. Renormalization factors : ( ) Ward-Takahashi identity 23
24 WZ Bare action vertices and counterterms residues x_1, x_2 beta function ordinary counterterms new vertices and new counterterms Bare Weyl action Wess-Zumino action for conformal anomaly 24
25 Laurent expansion of b Euler term Positive constant counterterms Wess-Zumino action and new counterterms Riegert Conformal mode dynamics 25
26 Hathrell Hathrell counterterm Hathrell, Ann.Phys.142(1982)34; Ann.Phys.139(1982)136 3-loop b c D 26
27 diff. inv. quantum gravity+qed where : momentum defined on the flat metric asymptotic freedom : : with 27
28 + = UV finite z: small fictitious mass (IR regularization) cancel out! propagator 28
29 Two-point function of e^4 Vertex function ( ) of e^6 And also, two-point function of e^6 29
30 Einstein massive ghost Planck 30
31 Conformal Field Theory on R x S^3 from Quantized Gravity, arxiv: [hep-th]
32 t Weyl radiation gauge Conformal Killing vector 15 32
33 Wess-Zumino 2 Mode expansion Dirac quantization where 33
34 SU(2)xSU(2) Clebsch-Gordan Riegert Weyl 34
35 Confomal symmetry = diffeomorphism invariance = Wheeler-DeWitt then vacuum state pure imaginary 35
36 2 Physical states Diffeomorphism invariant fields = Scalar curvature operator (at large b_1) Using the correlation function A>0 b_1 > 0 (right sign of WZ action) 36
37 From CFT Spectra to CMB Multipoles in Quantum Gravity Cosmology, arxiv: [astro-ph] with S. Horata and T. Yukawa
38 = Einstein 38
39 (WZ + Einstein) WZ action Planck Friedmann 39
40 Wess-Zumino proper time where WZ 40
41 Hubble Einstein Hubble 41
42 4 Big bang H, ρ ρ H Friedman proper time,τ 42
43 Einstein (derivative expansion) tree + 1-loop tree cf. chiral perturbation theory Einstein 1-loop : irrelevant 43
44 e-foldings : 44
45 45
46 Bardeen s gravitational potentials Evolution equation for gravitational potentials Constraint equation initially finally 46
47 CFT In Fourier space Delta function In Fourier space Harrison-Zel dovich-peebles spectrum for GUT models 47
48 Bardeen Potential Φ(b 1 =10, m=0.0156) proper time, log 10 (τ/τ p ) k [Mpc -1 ] proper time τ k [Mpc -1 ]
49 Non-Gaussianity in initial CFT spectrum In Fourier space non-gaussinity parameter is diffeomorphism inv. 49
50 Tensor Perturbation (b 1 =10, m=0.0156) Initial CFT spectrum k [Mpc -1 ] proper time, log 10 (τ/τ p ) 50
51 1 running coupling k Index running coupling 51
52 TT power spectrum wmap 5yrs acbar
53 TE power spectrum
54
55 CFT CFT 3 55
56 CMB 56
57 DT String susceptibility Crumple Phase Dimple Phase Horata, Egawa, Yukawa (2002) 57
58
59 Canonical Quantization on R x S^3 R x S^3 background metric ( mode-expansions become simple) Isometry of S^3 = SU(2)xSU(2) Tensor harmonics that belongs to rep. with Laplacian on S^3 59
60 Conformal Algebra on R x S^3 The generator of conformal algebra Time translation: Rotation on S^3: Special conformal: 15 conformal Killing vectors on R x S^3 60
61 Conformal Algebra on R x S^3 Conformal algebra 15 generators : Hamiltonian : S^3 rotation : special conf. + dilatation transf. [=4 vectors of SO(4)] 6 generators of SU(2)xSU(2) 61
62 Traceless Tensor Fields Traceless tensor mode is decomposed as Take transverse gauge by using the four gauge parameters Gauge-fixed Weyl action Furthermore, we take radiation gauge+ residual gauge DOF = conformal symmetry 62
63 Vector harmonics = rep. with Tensor harmonics = rep. with (polarizations) Transverse-traceless tensor mode Transverse vector mode Commutators 63
64 The generators of conformal algebra ( ) SU(2)^2 CG coeff. : STT type : STV type : SVV type Conformal symmetry mixes all tensor modes. Emphasize that negative-metric modes are indispensable to form the close algebra of conformal symmetry quantum mechanically 64
2 Planck Planck BRST Planck Λ QG Planck GeV Planck Λ QG Friedmann CMB
量子重力理論と宇宙論 (下巻) くりこみ理論と初期宇宙論 浜田賢二 高エネルギー加速器研究機構 (KEK) 素粒子原子核研究所 http://research.kek.jp/people/hamada/ 量子重力の世界は霧に包まれた距離感のない幽玄の世界にたとえること ができる 深い霧が晴れて時空が現れる 国宝松林図屏風 (長谷川等伯筆) 平成 20 年 11 月初版/平成 21 年 09 月改定/
q quark L left-handed lepton. λ Gell-Mann SU(3), a = 8 σ Pauli, i =, 2, 3 U() T a T i 2 Ỹ = 60 traceless tr Ỹ 2 = 2 notation. 2 off-diagonal matrices
Grand Unification M.Dine, Supersymmetry And String Theory: Beyond the Standard Model 6 2009 2 24 by Standard Model Coupling constant θ-parameter 8 Charge quantization. hypercharge charge Gauge group. simple
1. Introduction Palatini formalism vierbein e a µ spin connection ω ab µ Lgrav = e (R + Λ). 16πG R µνab µ ω νab ν ω µab ω µac ω νcb + ω νac ω µcb, e =
Chiral Fermion in AdS(dS) Gravity Fermions in (Anti) de Sitter Gravity in Four Dimensions, N.I, Takeshi Fukuyama, arxiv:0904.1936. Prog. Theor. Phys. 122 (2009) 339-353. 1. Introduction Palatini formalism
Introduction SFT Tachyon condensation in SFT SFT ( ) at 1 / 38
( ) 2011 5 14 at 1 / 38 Introduction? = String Field Theory = SFT 2 / 38 String Field : ϕ(x, t) x ϕ x / ( ) X ( σ) (string field): Φ[X(σ), t] X(σ) Φ (Φ X(σ) ) X(σ) & / 3 / 38 SFT with Lorentz & Gauge Invariance
Einstein ( ) YITP
Einstein ( ) 2013 8 21 YITP 0. massivegravity Massive spin 2 field theory Fierz-Pauli (FP ) Kinetic term L (2) EH = 1 2 [ λh µν λ h µν λ h λ h 2 µ h µλ ν h νλ + 2 µ h µλ λ h], (1) Mass term FP L mass =
inflation.key
2 2 G M 0 0-5 ϕ / M G 0 L SUGRA = 1 2 er + eg ij Dµ φ i Dµ φ j 1 2 eg2 D (a) D +ieg ij χ j σ µ Dµ χ i + eϵ µνρσ ψ µ σ ν Dρ ψ σ 1 4 ef (ab) R F (a) [ ] + i 2 e λ (a) σ µ Dµ λ (a) + λ (a) σ µ Dµ λ (a) 1
main.dvi
SGC - 48 208X Y Z Z 2006 1930 β Z 2006! 1 2 3 Z 1930 SGC -12, 2001 5 6 http://www.saiensu.co.jp/support.htm http://www.shinshu-u.ac.jp/ haru/ xy.z :-P 3 4 2006 3 ii 1 1 1.1... 1 1.2 1930... 1 1.3 1930...
main.dvi
Ver. 1.50 2001 ( ) 1 4 2 Effective Theory 5 2.1 Effective theory... 5 2.2 massless 2-flavor QCD... 5 2.3..................... 9 2.4 Standard model... 10 2.5... 11 2.6... 13 3 Supersymmetry 15 3.1 Supersymmetry...
SUSY DWs
@ 2013 1 25 Supersymmetric Domain Walls Eric A. Bergshoeff, Axel Kleinschmidt, and Fabio Riccioni Phys. Rev. D86 (2012) 085043 (arxiv:1206.5697) ( ) Contents 1 2 SUSY Domain Walls Wess-Zumino Embedding
OTO研究会スライド
OTO @, 2017 5 26 2 CFT OTO ) PTEP 2016 (2016) no.11, 113B06 (arxiv1602.06542[hep-th]) Collaboration with P. Caputa(YITP) and A.Veliz-Osorio(Queen Mary U.) i i +1 H = X i i z z i+1 + h X i i x i z = 1
Kaluza-Klein(KK) SO(11) KK 1 2 1
Maskawa Institute, Kyoto Sangyo University Naoki Yamatsu 2016 4 12 ( ) @ Kaluza-Klein(KK) SO(11) KK 1 2 1 1. 2. 3. 4. 2 1. 標準理論 物質場 ( フェルミオン ) スカラー ゲージ場 クォーク ヒッグス u d s b ν c レプトン ν t ν e μ τ e μ τ e h
[ ] = L [δ (D ) (x )] = L D [g ] = L D [E ] = L Table : ħh = m = D D, V (x ) = g δ (D ) (x ) E g D E (Table )D = Schrödinger (.3)D = (regularization)
![[ ] = L [δ (D ) (x )] = L D [g ] = L D [E ] = L Table : ħh = m = D D, V (x ) = g δ (D ) (x ) E g D E (Table )D = Schrödinger (.3)D = (regularization)](/thumbs/47/23763429.jpg "[ ] = L [δ (D ) (x )] = L D [g ] = L D [E ] = L Table : ħh = m = D D, V (x ) = g δ (D ) (x ) E g D E (Table )D = Schrödinger (.3)D = (regularization)")
. D............................................... : E = κ ............................................ 3.................................................
(check matrices and minimum distances) H : a check matrix of C the minimum distance d = (the minimum # of column vectors of H which are linearly depen
Hamming (Hamming codes) c 1 # of the lines in F q c through the origin n = qc 1 q 1 Choose a direction vector h i for each line. No two vectors are colinear. A linearly dependent system of h i s consists
master.dvi
pp-wave 003 0 4 AdS/CF T CFT 6. AdS/CF T..................................... 6. 4 Conformal Field Theory........................... 8.. Conformal............................... 8.. CFT...................................
kougiroku7_26.dvi
2005 : D-brane tachyon : ( ) 2005 8 7 8 :,,,,,,, 1 2 1.1 Introduction............................... 2 1.2......................... 6 1.3 Second Revolution (1994 )................... 11 2 Type II 26 2.1
4/15 No.
4/15 No. 1 4/15 No. 4/15 No. 3 Particle of mass m moving in a potential V(r) V(r) m i ψ t = m ψ(r,t)+v(r)ψ(r,t) ψ(r,t) = ϕ(r)e iωt ψ(r,t) Wave function steady state m ϕ(r)+v(r)ϕ(r) = εϕ(r) Eigenvalue problem
φ 4 Minimal subtraction scheme 2-loop ε 2008 (University of Tokyo) (Atsuo Kuniba) version 21/Apr/ Formulas Γ( n + ɛ) = ( 1)n (1 n! ɛ + ψ(n + 1)
φ 4 Minimal subtraction scheme 2-loop ε 28 University of Tokyo Atsuo Kuniba version 2/Apr/28 Formulas Γ n + ɛ = n n! ɛ + ψn + + Oɛ n =,, 2, ψn + = + 2 + + γ, 2 n ψ = γ =.5772... Euler const, log + ax x
untitled
20 11 1 KEK 2 (cosmological perturbation theory) CMB R. Durrer, The theory of CMB Anisotropies, astro-ph/0109522; A. Liddle and D. Lyth, Cosmological Inflation and Large-Scale Structure (Cambridge University
離散研究会2013
2013 9 27-30, S. Carlip, Challenges for Emergent Gravity, arxiv:1207.2504 [gr-qc] Wheeler-DeWitt N= M abc,p abc a, b, c =1, 2,...,N M abc = M bca = M bac O(N) N.Sasakura, Quantum canonical tensor model
untitled
kajino@nao.ac.jp http://th.nao.ac.jp/~gkajino/? BIG-BANG! STARS SUPERNOVAE? R-PROCESS COSMIC-RAYS R S N=50) R S N=82) R S N=126) ++ + Actinide AGB STARS S-PROCESS 232 Th (14.05Gy) P 238 U (4.47 Gy) SUPERNOVA-γ
Isogai, T., Building a dynamic correlation network for fat-tailed financial asset returns, Applied Network Science (7):-24, 206,
H28. (TMU) 206 8 29 / 34 2 3 4 5 6 Isogai, T., Building a dynamic correlation network for fat-tailed financial asset returns, Applied Network Science (7):-24, 206, http://link.springer.com/article/0.007/s409-06-0008-x
Seiberg Witten 1994 N = 2 SU(2) Yang-Mills 1 1 3 2 5 2.1..................... 5 2.2.............. 8 2.3................................. 9 3 N = 2 Yang-Mills 11 3.1............................... 11 3.2
A Higher Weissenberg Number Analysis of Die-swell Flow of Viscoelastic Fluids Using a Decoupled Finite Element Method Iwata, Shuichi * 1/Aragaki, Tsut
A Higher Weissenberg Number Analysis of Die-swell Flow of Viscoelastic Fluids Using a Decoupled Finite Element Method Iwata, Shuichi * 1/Aragaki, Tsutomu * 1/Mori, Hideki * 1 Ishikawa, Satoshi * 1/Shin,
中央大学セミナー.ppt
String Gas Cosmology References Brandenberger & Vafa, Superstrings in the early universe, Nucl.Phys.B316(1988) 391. Tseytlin & Vafa, Elements of string cosmology, Nucl.Phys.B372 (1992) 443. Brandenberger,
ADM-Hamiltonian Cheeger-Gromov 3. Penrose
ADM-Hamiltonian 1. 2. Cheeger-Gromov 3. Penrose 0. ADM-Hamiltonian (M 4, h) Einstein-Hilbert M 4 R h hdx L h = R h h δl h = 0 (Ric h ) αβ 1 2 R hg αβ = 0 (Σ 3, g ij ) (M 4, h ij ) g ij, k ij Σ π ij = g(k
02-量子力学の復習
4/17 No. 1 4/17 No. 2 4/17 No. 3 Particle of mass m moving in a potential V(r) V(r) m i ψ t = 2 2m 2 ψ(r,t)+v(r)ψ(r,t) ψ(r,t) Wave function ψ(r,t) = ϕ(r)e iωt steady state 2 2m 2 ϕ(r)+v(r)ϕ(r) = εϕ(r)
G (n) (x 1, x 2,..., x n ) = 1 Dφe is φ(x 1 )φ(x 2 ) φ(x n ) (5) N N = Dφe is (6) G (n) (generating functional) 1 Z[J] d 4 x 1 d 4 x n G (n) (x 1, x 2
![G (n) (x 1, x 2,..., x n ) = 1 Dφe is φ(x 1 )φ(x 2 ) φ(x n ) (5) N N = Dφe is (6) G (n) (generating functional) 1 Z[J] d 4 x 1 d 4 x n G (n) (x 1, x 2](/thumbs/91/105326061.jpg "G (n) (x 1, x 2,..., x n ) = 1 Dφe is φ(x 1 )φ(x 2 ) φ(x n ) (5) N N = Dφe is (6) G (n) (generating functional) 1 Z[J] d 4 x 1 d 4 x n G (n) (x 1, x 2")
6 Feynman (Green ) Feynman 6.1 Green generating functional Z[J] φ 4 L = 1 2 µφ µ φ m 2 φ2 λ 4! φ4 (1) ( 1 S[φ] = d 4 x 2 φkφ λ ) 4! φ4 (2) K = ( 2 + m 2 ) (3) n G (n) (x 1, x 2,..., x n ) = φ(x 1 )φ(x
磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論
email: takahash@sci.u-hyogo.ac.jp May 14, 2009 Outline 1. 2. 3. 4. 5. 6. 2 / 262 Today s Lecture: Mode-mode Coupling Theory 100 / 262 Part I Effects of Non-linear Mode-Mode Coupling Effects of Non-linear
スケーリング理論とはなにか? - --尺度を変えて見えること--
? URL: http://maildbs.c.u-tokyo.ac.jp/ fukushima mailto:hukusima@phys.c.u-tokyo.ac.jp DEX-SMI @ 2006 12 17 ( ) What is scaling theory? DEX-SMI 1 / 40 Outline Outline 1 2 3 4 ( ) What is scaling theory?
' , 24 :,,,,, ( ) Cech Index theorem 22 5 Stability 44 6 compact 49 7 Donaldson 58 8 Symplectic structure 63 9 Wall crossing 66 1
1998 1998 7 20 26, 44. 400,,., (KEK), ( ) ( )..,.,,,. 1998 1 '98 7 23, 24 :,,,,, ( ) 1 3 2 Cech 6 3 13 4 Index theorem 22 5 Stability 44 6 compact 49 7 Donaldson 58 8 Symplectic structure 63 9 Wall crossing
1 ( ) Einstein, Robertson-Walker metric, R µν R 2 g µν + Λg µν = 8πG c 4 T µν, (1) ( ds 2 = c 2 dt 2 + a(t) 2 dr 2 ) + 1 Kr 2 r2 dω 2, (2) (ȧ ) 2 H 2
1 ( ) Einstein, Robertson-Walker metric, R µν R 2 g µν + Λg µν = 8πG c 4 T µν, (1) ( ds 2 = c 2 dt 2 + a(t) 2 dr 2 ) + 1 Kr 2 r2 dω 2, (2) (ȧ ) 2 H 2 = 8πG a 3c 2 ρ Kc2 a 2 + Λc2 3 (3), ä a = 4πG Λc2 (ρ
untitled
1 Constructive field theory and renormalization group Hiroshi WATANABE 1 2001 7,. 1 2 2 Euclidean field theory 3 2.1...................................... 4 2.2..................................... 6 3
Yang-Mills Yang-Mills Yang-Mills 50 operator formalism operator formalism 1 I The Dawning of Gauge T
Yang-Mills 50 E-mail: kugo@yukawa.kyoto-u.ac.jp 2004 Yang-Mills 50 2004 Yang-Mills 50 operator formalism operator formalism 1 I The Dawning of Gauge Theory O Raifeartaigh [1] I, II, III O Raifeartaigh
nenmatsu5c19_web.key
KL π ± e νe + e - (Ke3ee) Ke3ee ν e + e - Ke3 K 0 γ e + π - Ke3 KL ; 40.67(%) Ke3ee K 0 ν γ e + π - Ke3 KL ; 40.67(%) Me + e - 10 4 10 3 10 2 : MC Ke3γ : data K L real γ e detector matter e e 10 1 0 0.02
,,.,,.,.,,,.,.,.,..,.,,.,.,,..,, CMB
,,.,,.,.,,,.,.,.,..,.,,.,.,,..,,. 1 3 2 3 2.1............................................. 3 2.2 CMB............................................... 5 2.3........................................... 7 2.4.............................................
& Vol.5 No (Oct. 2015) TV 1,2,a) , Augmented TV TV AR Augmented Reality 3DCG TV Estimation of TV Screen Position and Ro
TV 1,2,a) 1 2 2015 1 26, 2015 5 21 Augmented TV TV AR Augmented Reality 3DCG TV Estimation of TV Screen Position and Rotation Using Mobile Device Hiroyuki Kawakita 1,2,a) Toshio Nakagawa 1 Makoto Sato
1.1 foliation M foliation M 0 t Σ t M M = t R Σ t (12) Σ t t Σ t x i Σ t A(t, x i ) Σ t n µ Σ t+ t B(t + t, x i ) AB () tα tαn µ Σ t+ t C(t + t,
1 Gourgoulhon BSSN BSSN ϕ = 1 6 ( D i β i αk) (1) γ ij = 2αĀij 2 3 D k β k γ ij (2) K = e 4ϕ ( Di Di α + 2 D i ϕ D i α ) + α ] [4π(E + S) + ĀijĀij + K2 3 (3) Ā ij = 2 3Āij D k β k 2αĀikĀk j + αāijk +e
1 Affine Lie 1.1 Affine Lie g Lie, 2h A B = tr g ad A ad B A, B g Killig form., h g daul Coxeter number., g = sl n C h = n., g long root 2 2., ρ half
Wess-Zumino-Witten 1999 3 18 Wess-Zumino-Witten., Knizhnik-Zamolodchikov-Bernard,,. 1 Affine Lie 2 1.1 Affine Lie.............................. 2 1.2..................................... 3 2 WZW 4 3 Knizhnik-Zamolodchikov-Bernard
量子重力理論と宇宙論 (上巻) 共形場理論と重力の量子論 浜田賢二 高エネルギー加速器研究機構 (KEK) 素粒子原子核研究所 量子重力の世界は霧に包まれた距離感のない幽玄の世界にたとえること ができる 深い霧が晴れて時空が
量子重力理論と宇宙論 (上巻) 共形場理論と重力の量子論 浜田賢二 高エネルギー加速器研究機構 (KEK) 素粒子原子核研究所 http://research.kek.jp/people/hamada/ 量子重力の世界は霧に包まれた距離感のない幽玄の世界にたとえること ができる 深い霧が晴れて時空が現れる 国宝松林図屏風 (長谷川等伯筆) 平成 0 年 11 月初版/平成 1 年 09 月改定/ 平成
200708_LesHouches_02.ppt
Numerical Methods for Geodynamo Simulation Akira Kageyama Earth Simulator Center, JAMSTEC, Japan Part 2 Geodynamo Simulations in a Sphere or a Spherical Shell Outline 1. Various numerical methods used
THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE.
THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE. E-mail: {ytamura,takai,tkato,tm}@vision.kuee.kyoto-u.ac.jp Abstract Current Wave Pattern Analysis for Anomaly
3 exotica
( / ) 2013 2 23 embedding tensors (non)geometric fluxes exotic branes + D U-duality G 0 R-symmetry H dim(g 0 /H) T-duality 11 1 1 0 1 IIA R + 1 1 1 IIB SL(2, R) SO(2) 2 1 9 GL(2, R) SO(2) 3 SO(1, 1) 8
318 T. SICE Vol.52 No.6 June 2016 (a) (b) (c) (a) (c) ) 11) (1) (2) 1 5) 6) 7), 8) 5) 20 11) (1
Vol.52, No.6, 317/329 2016 Mathematical Model and Analysis on Human s Handwork and Their Application to Brush Motion and Junkatsu of Japanese Calligraphy Tadamichi Mawatari and Kensuke Tsuchiya There is
Hilbert, von Neuman [1, p.86] kt 2 1 [1, 2] 2 2
![Hilbert, von Neuman [1, p.86] kt 2 1 [1, 2] 2 2](/thumbs/91/105692760.jpg "Hilbert, von Neuman [1, p.86] kt 2 1 [1, 2] 2 2")
hara@math.kyushu-u.ac.jp 1 1 1.1............................................... 2 1.2............................................. 3 2 3 3 5 3.1............................................. 6 3.2...................................
CKY CKY CKY 4 Kerr CKY
( ) 1. (I) Hidden Symmetry and Exact Solutions in Einstein Gravity Houri-Y.Y: Progress Supplement (2011) (II) Generalized Hidden Symmetries and Kerr-Sen Black Hole Houri-Kubiznak-Warnick-Y.Y: JHEP (2010)
/ Christopher Essex Radiation and the Violation of Bilinearity in the Thermodynamics of Irreversible Processes, Planet.Space Sci.32 (1984) 1035 Radiat
/ Christopher Essex Radiation and the Violation of Bilinearity in the Thermodynamics of Irreversible Processes, Planet.Space Sci.32 (1984) 1035 Radiation and the Continuing Failure of the Bilinear Formalism,
h23w1.dvi
24 I 24 2 8 10:00 12:30 1),. Do not open this problem booklet until the start of the examination is announced. 2) 3.. Answer the following 3 problems. Use the designated answer sheet for each problem.
YITP50.dvi
1 70 80 90 50 2 3 3 84 first revolution 4 94 second revolution 5 6 2 1: 1 3 consistent 1-loop Feynman 1-loop Feynman loop loop loop Feynman 2 3 2: 1-loop Feynman loop 3 cycle 4 = 3: 4: 4 cycle loop Feynman
Fig. 3 Flow diagram of image processing. Black rectangle in the photo indicates the processing area (128 x 32 pixels).
Fig. 1 The scheme of glottal area as a function of time Fig. 3 Flow diagram of image processing. Black rectangle in the photo indicates the processing area (128 x 32 pixels). Fig, 4 Parametric representation
D.dvi
2005 3 3 1 7 1.1... 7 1.2 Brane... 8 1.3 AdS/CFT black hole... 9 1.4... 10 2 11 2.1 Kaluza-Klein... 11 2.1.1 Kazula-Klein 4... 11 2.1.2 Kaluza-Klein... 13 2.2 Brane... 14 2.2.1 Brane 4... 14 2.2.2 Bulk
Fig. 3 Coordinate system and notation Fig. 1 The hydrodynamic force and wave measured system Fig. 2 Apparatus of model testing
The Hydrodynamic Force Acting on the Ship in a Following Sea (1 St Report) Summary by Yutaka Terao, Member Broaching phenomena are most likely to occur in a following sea to relative small and fast craft
TeV b,c,τ KEK/ ) ICEPP
TeV b,c,τ KEK/ ) ICEPP 2 TeV TeV ~1930 ~1970 ~2010 LHC TeV LHC TeV LHC TeV CKM K FCNC K CP violation c b, τ B-B t B CP violation interplay 6 Super B Factory Super KEKB LoI (hep-ex/0406071) SLAC Super B
Lagrange.dvi
Lagrange 1 2006.2.10 1 Introduction CfA survey 2dF SDSS high-z Euler Lagrange Lagrange CDM Lagrange Lagrange 2 Newton Friedmann Newton Newton Newton [1,2,3,4,5] ρ + r ρu = 0, 1 t r u +u r u = 1 t r ρ rp
Developement of Plastic Collocation Method Extension of Plastic Node Method by Yukio Ueda, Member Masahiko Fujikubo, Member Masahiro Miura, Member Sum
Developement of Plastic Collocation Method Extension of Plastic Node Method by Yukio Ueda, Member Masahiko Fujikubo, Member Masahiro Miura, Member Summary Previously, the authors developed the plastic
Gravothermal Catastrophe & Quasi-equilibrium Structure in N-body Systems
2004/3/1 3 N 1 Antonov Problem & Quasi-equilibrium State in N-body N Systems A. Taruya (RESCEU, Univ.Tokyo) M. Sakagami (Kyoto Univ.) 2 Antonov problem N-body study of quasi-attractivity M15 T Antonov
1. 1.1....................... 1.2............................ 1.3.................... 1.4.................. 2. 2.1.................... 2.2..................... 2.3.................... 3. 3.1.....................
BH BH BH BH Typeset by FoilTEX 2
GR BH BH 2015.10.10 BH at 2015.09.07 NICT 2015.05.26 Typeset by FoilTEX 1 BH BH BH BH Typeset by FoilTEX 2 1. BH 1.1 1 Typeset by FoilTEX 3 1.2 2 A B A B t = 0 A: m a [kg] B: m b [kg] t = t f star free
Chern-Simons Jones 3 Chern-Simons 1 - Chern-Simons - Jones J(K; q) [1] Jones q 1 J (K + ; q) qj (K ; q) = (q 1/2 q
![Chern-Simons Jones 3 Chern-Simons 1 - Chern-Simons - Jones J(K; q) [1] Jones q 1 J (K + ; q) qj (K ; q) = (q 1/2 q](/thumbs/94/118766307.jpg "Chern-Simons Jones 3 Chern-Simons 1 - Chern-Simons - Jones J(K; q) [1] Jones q 1 J (K + ; q) qj (K ; q) = (q 1/2 q")
Chern-Simons E-mail: fuji@th.phys.nagoya-u.ac.jp Jones 3 Chern-Simons - Chern-Simons - Jones J(K; q) []Jones q J (K + ; q) qj (K ; q) = (q /2 q /2 )J (K 0 ; q), () J( ; q) =. (2) K Figure : K +, K, K 0
Abstract This paper concerns with a method of dynamic image cognition. Our image cognition method has two distinguished features. One is that the imag
2004 RGB A STUDY OF RGB COLOR INFORMATION AND ITS APPLICATION 03R3237 Abstract This paper concerns with a method of dynamic image cognition. Our image cognition method has two distinguished features. One
PowerPoint Presentation
2010 KEK (Japan) (Japan) (Japan) Cheoun, Myun -ki Soongsil (Korea) Ryu,, Chung-Yoe Soongsil (Korea) 1. S.Reddy, M.Prakash and J.M. Lattimer, P.R.D58 #013009 (1998) Magnetar : ~ 10 15 G ~ 10 17 19 G (?)
: u i = (2) x i Smagorinsky τ ij τ [3] ij u i u j u i u j = 2ν SGS S ij, (3) ν SGS = (C s ) 2 S (4) x i a u i ρ p P T u ν τ ij S c ν SGS S csgs
![: u i = (2) x i Smagorinsky τ ij τ [3] ij u i u j u i u j = 2ν SGS S ij, (3) ν SGS = (C s ) 2 S (4) x i a u i ρ p P T u ν τ ij S c ν SGS S csgs](/thumbs/91/106610562.jpg ": u i = (2) x i Smagorinsky τ ij τ [3] ij u i u j u i u j = 2ν SGS S ij, (3) ν SGS = (C s ) 2 S (4) x i a u i ρ p P T u ν τ ij S c ν SGS S csgs")
15 C11-4 Numerical analysis of flame propagation in a combustor of an aircraft gas turbine, 4-6-1 E-mail: tominaga@icebeer.iis.u-tokyo.ac.jp, 2-11-16 E-mail: ntani@iis.u-tokyo.ac.jp, 4-6-1 E-mail: itoh@icebeer.iis.u-tokyo.ac.jp,
ssastro2016_shiromizu
26 th July 2016 / 1991(M1)-1995(D3), 2005( ) 26 th July 2016 / 1. 2. 3. 4. . ( ) 1960-70 1963 Kerr 1965 BH Penrose 1967 Hawking BH Israel 1971 (Carter)-75(Robinson) BH 1972 BH theorem(,, ) Hawk 1975 Hawking
2012専門分科会_new_4.pptx
d dt L L = 0 q i q i d dt L L = 0 r i i r i r r + Δr Δr δl = 0 dl dt = d dt i L L q i q i + q i i q i = q d L L i + q i i dt q i i q i = i L L q i L = 0, H = q q i L = E i q i i d dt L q q i i L = L(q
橋本研
-Goldstone ( ) 2011 4-2012 3 -Goldstone UV IR SSB+ : Chiral Lagrangian :,... -Goldstone Nambu( 60), Goldstone(61), Nambu, Jona-Lasinio( 61), Goldstone, Salam, Weinberg( 62) Lorentz ( ) = NG 2002~2004?
Ï¢À±ÃæÀŁ»ÒÀ±¤ª¤è¤Ó¥Ö¥é¥Ã¥¯¥Û¡¼¥ë¡ÝÃæÀŁ»ÒÀ±Ï¢À±¤Î¹çÂÎ ¡Á ½àÊ¿¹Õ²ò¤Î¸¦µæ¤Î¸½¾õ¤Èº£¸å¤ÎŸ˾ ¡Á
2009 10 15 (UWM) 2009 10 15 2 / 35 1 2 Corotation Irrotation 3 4 (UWM) 2009 10 15 3 / 35 10 100/yr (D = 300 Mpc) 1 40/yr (D = 300 Mpc) GWs 1 700/yr (D = 300 Mpc) X BH NS LIGO (UWM) 2009 10 15 4 / 35 (UWM)
1 Fig. 1 Extraction of motion,.,,, 4,,, 3., 1, 2. 2.,. CHLAC,. 2.1,. (256 ).,., CHLAC. CHLAC, HLAC. 2.3 (HLAC ) r,.,. HLAC. N. 2 HLAC Fig. 2
CHLAC 1 2 3 3,. (CHLAC), 1).,.,, CHLAC,.,. Suspicious Behavior Detection based on CHLAC Method Hideaki Imanishi, 1 Toyohiro Hayashi, 2 Shuichi Enokida 3 and Toshiaki Ejima 3 We have proposed a method for
Table 1. Assumed performance of a water electrol ysis plant. Fig. 1. Structure of a proposed power generation system utilizing waste heat from factori
Proposal and Characteristics Evaluation of a Power Generation System Utilizing Waste Heat from Factories for Load Leveling Pyong Sik Pak, Member, Takashi Arima, Non-member (Osaka University) In this paper,
CMP Technical Report No. 4 Department of Computational Nanomaterials Design ISIR, Osaka University 2 2................................. 2.2......................... 2 3 3 3................................
cm λ λ = h/p p ( ) λ = cm E pc [ev] 2.2 quark lepton u d c s t b e 1 3e electric charge e color charge red blue green qq
![cm λ λ = h/p p ( ) λ = cm E pc [ev] 2.2 quark lepton u d c s t b e 1 3e electric charge e color charge red blue green qq](/thumbs/89/98710373.jpg "cm λ λ = h/p p ( ) λ = cm E pc [ev] 2.2 quark lepton u d c s t b e 1 3e electric charge e color charge red blue green qq")
2007 2007 7 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1 2007 2 4 5 6 6 2 2.1 1: KEK Web page 1 1 1 10 16 cm λ λ = h/p p ( ) λ = 10 16 cm E pc [ev] 2.2 quark lepton 2 2.2.1 u d c s t b + 2 3 e 1 3e electric charge
CP-PACS CP-PACS CP-PACS : 2048PU+128IOU 614GFLOPS peak 128GByte memory 1058GByte disk 1992 1996 SR2201 : 1996 8 9 CP-PACS Top 500 List ranking No. 1 November 1996 Linpack 368.2Gflops No. 24 Novermber 1999
QCD 1 QCD GeV 2014 QCD 2015 QCD SU(3) QCD A µ g µν QCD 1
QCD 1 QCD GeV 2014 QCD 2015 QCD SU(3) QCD A µ g µν QCD 1 (vierbein) QCD QCD 1 1: QCD QCD Γ ρ µν A µ R σ µνρ F µν g µν A µ Lagrangian gr TrFµν F µν No. Yes. Yes. No. No! Yes! [1] Nash & Sen [2] Riemann
Introduction 2 / 43
Batalin-Vilkoviski ( ) 2016 2 22 at SFT16 based on arxiv:1511.04187 BV Analysis of Tachyon Fluctuation around Multi-brane Solutions in Cubic String Field Theory 1 / 43 Introduction 2 / 43 in Cubic open
Fig.l Music score for ensemble Fig.Z Definition of each indicator Table I Correlation coefficient between hitting lag variation /,(n) and hitting cycl
It is difficult problem to make a human like ensemble system, In this research, we analyzed the rhythm interaction between performers by measure the hutting time and hitting cycle of keyboard performance.
宇宙の背景輻射 現在 150億年 50億年 星や銀河の 形成 自然界には４つの力 3つの分岐点が今回のシリーズの目標 3K LHC温度 1016K (10-12 ~ 10-14s) 10億年 (2) GUTへの挑戦 超対称性による大統一 3000K 30万年 原子 分子の形成 3分 原子核の形成 10-10 秒 弱い相互作用が分離 ３つの力が分離する 量子重力の世界 10-34 秒 10-43 秒
COE
COE COOL05 MD @ @ @ @ n ν x, y 2 2 International Workshop on Beam Cooling and Related Topics ( COOL05) General Topics Overview. S-LSR Report from Lab Report from Lab Electron Cooling Muon Cooling
Mikio Yamamoto: Dynamical Measurement of the E-effect in Iron-Cobalt Alloys. The AE-effect (change in Young's modulus of elasticity with magnetization
Mikio Yamamoto: Dynamical Measurement of the E-effect in Iron-Cobalt Alloys. The AE-effect (change in Young's modulus of elasticity with magnetization) in the annealed state of iron-cobalt alloys has been
空力騒音シミュレータの開発
41 COSMOS-V, an Aerodynamic Noise Simulator Nariaki Horinouchi COSMOS-V COSMOS-V COSMOS-V 3 The present and future computational problems of the aerodynamic noise analysis using COSMOS-V, our in-house
29 7 5 i 1 1 1.1............................ 1 1.1.1................. 1 1.1.2............................. 3 1.1.3......................... 4 1.2........................... 9 1.2.1................. 9
Numerical Analysis II, Exam End Term Spring 2017
H. Ammari W. Wu S. Yu Spring Term 2017 Numerical Analysis II ETH Zürich D-MATH End Term Spring 2017 Problem 1 Consider dx = f(t, x), t [0, T ] dt x(0) = x 0 R [28 Marks] with f C subject to the Lipschitz
80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = i=1 i=1 n λ x i e λ i=1 x i! = λ n i=1 x i e nλ n i=1 x
80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = n λ x i e λ x i! = λ n x i e nλ n x i! n n log l(λ) = log(λ) x i nλ log( x i!) log l(λ) λ = 1 λ n x i n =
2 2 Belavin Polyakov Zamolodchikov (BPZ) 1984 [13] 2 BPZ BPZ Virasoro [16][18] [20], [30], [47] [1][6] [8][10], [11], [12] Affine [6],GKO [2] W
![2 2 Belavin Polyakov Zamolodchikov (BPZ) 1984 [13] 2 BPZ BPZ Virasoro [16][18] [20], [30], [47] [1][6] [8][10], [11], [12] Affine [6],GKO [2] W](/thumbs/91/105488419.jpg "2 2 Belavin Polyakov Zamolodchikov (BPZ) 1984 [13] 2 BPZ BPZ Virasoro [16][18] [20], [30], [47] [1][6] [8][10], [11], [12] Affine [6],GKO [2] W")
SGC -83 2 2 Belavin Polyakov Zamolodchikov (BPZ) 1984 [13] 2 BPZ BPZ 1 3 4 Virasoro [16][18] [20], [30], [47] [1][6] [8][10], [11], [12] Affine [6],GKO [2] W [14] c = 1 CFT [8] Rational CFT [15], [56]
·«¤ê¤³¤ß·²¤È¥ß¥ì¥Ë¥¢¥àÌäÂê
.. 1 10-11 Nov., 2016 1 email:keiichi.r.ito@gmail.com, ito@kurims.kyoto-u.ac.jp ( ) 10-11 Nov., 2016 1 / 45 Clay Institute.1 Construction of 4D YM Field Theory (Jaffe, Witten) Jaffe, Balaban (1980).2 Solution
Euler, Yang-Mills Clebsch variable Helicity ( Tosiaki Kori ) School of Sciences and Technology, Waseda Uiversity (i) Yang-Mills 3 A T (T A) Poisson Ha
Euler, Yang-ills Clebsch variable Helicity Tosiaki Kori ) School of Sciences and Technology, Waseda Uiversity i) Yang-ills 3 A T T A) Poisson Hamilton ii) Clebsch parametrization iii) Y- Y-iv) Euler,v)
.I.v e pmd
Structural Design for Curved Panels by Laminated Composite Materials (Identification of Lamination Parameters Using Modal Testing Method ) Tetsuya NARISAWA, Shohei IWATA Abstract - Using a modal testing
l ηµν hµν g µν = η µν + h µν, h µν 1 l Transvers-Traceless (TT) h TT 0µ = 0, η ij i h TT jk = 0, η ij h TT ij = 0, η µν µ ν h TT ij = 2 c 2 t + Δ 2 h TT = 0 ij 2 Polarization l From the TT condition, h
QOL
27.8.8 8.9 QOL How to How to How to How to How to 7 50 How to I think Yes 60 SF 11 21 26% 4 1 70 56 CGA CGA 80 3 54 297 400 60 70 3 21 22 22 ( ) ( ) 2.5 17 (1612) (1533-1615) 18 (1613) (1615) (1583-1644)
September 9, 2002 ( ) [1] K. Hukushima and Y. Iba, cond-mat/ [2] H. Takayama and K. Hukushima, cond-mat/020
![September 9, 2002 ( ) [1] K. Hukushima and Y. Iba, cond-mat/ [2] H. Takayama and K. Hukushima, cond-mat/020](/thumbs/94/118242373.jpg "September 9, 2002 ( ) [1] K. Hukushima and Y. Iba, cond-mat/ [2] H. Takayama and K. Hukushima, cond-mat/020")
mailto:hukusima@issp.u-tokyo.ac.jp September 9, 2002 ( ) [1] and Y. Iba, cond-mat/0207123. [2] H. Takayama and, cond-mat/0205276. Typeset by FoilTEX Today s Contents Against Temperature Chaos in Spin Glasses
『共形場理論』
T (z) SL(2, C) T (z) SU(2) S 1 /Z 2 SU(2) (ŜU(2) k ŜU(2) 1)/ŜU(2) k+1 ŜU(2)/Û(1) G H N =1 N =1 N =1 N =1 N =2 N =2 N =2 N =2 ĉ>1 N =2 N =2 N =4 N =4 1 2 2 z=x 1 +ix 2 z f(z) f(z) 1 1 4 4 N =4 1 = = 1.3
TQFT_yokota
, TY, Naito, Phys. Rev. B 99, 115106 (2019),, 2019 9 2 1 (DFT) (DFT)? HΨ(x 1,, x N ) = EΨ(x 1,, x N ) N DFT! Hohenberg, Kohn, PR (1964) Kohn, Sham, PRA (1965) (EDF) E[ρ] = F[ρ] + dxv(x)ρ(x) δe[ρ] δρ(x)
Influence of Material and Thickness of the Specimen to Stress Separation of an Infrared Stress Image Kenji MACHIDA The thickness dependency of the temperature image obtained by an infrared thermography
EQUIVALENT TRANSFORMATION TECHNIQUE FOR ISLANDING DETECTION METHODS OF SYNCHRONOUS GENERATOR -REACTIVE POWER PERTURBATION METHODS USING AVR OR SVC- Ju
EQUIVALENT TRANSFORMATION TECHNIQUE FOR ISLANDING DETECTION METHODS OF SYNCHRONOUS GENERATOR -REACTIVE POWER PERTURBATION METHODS USING AVR OR SVC- Jun Motohashi, Member, Takashi Ichinose, Member (Tokyo
Estimation of Photovoltaic Module Temperature Rise Motonobu Yukawa, Member, Masahisa Asaoka, Non-member (Mitsubishi Electric Corp.) Keigi Takahara, Me
Estimation of Photovoltaic Module Temperature Rise Motonobu Yukawa, Member, Masahisa Asaoka, Non-member (Mitsubishi Electric Corp.) Keigi Takahara, Member (Okinawa Electric Power Co.,Inc.) Toshimitsu Ohshiro,
06’ÓŠ¹/ŒØŒì
FD. FD FD FD FD FD FD / Plan-Do-See FD FD FD FD FD FD FD FD FD FD FD FD FD FD JABEE FD A. C. A B .. AV .. B Communication Space A FD FD ES FD FD The approach of the lesson improvement in Osaka City University
ÿþ
Abstract The aim of this paper is to describe 1. how media, especially mobile phones, have been utilized in childrearing practices, and 2. how the process of adoption influences the placement of techno-social
<8ED089EF8B D312D30914F95742E696E6464>
* 1 The problem of privacy in the news of newspapers and weekly magazines The analysis of the articles on the child serial killing incidents in Kobe Akihiko SHIMAZAKI Kenzo SHIDA Toshihiko KATANO *2 1
26 3 ( 29 5 ) D 3 1 (KEK) 1 Minkowski (conformal field theory, CFT) Minkowski Minkowski Hamilton Hermite Euclid
26 3 ( 29 5 ) D 3 (KEK) http://research.kek.jp/people/hamada/ Minkowski (conformal field theory, CFT) Minkowski Minkowski Hamilton Hermite Euclid Euclid Minkowski () Euclid Minkowski Euclid D 4 (, 206)
( ) URL: December 2, 2003
( ) URL: http://dbs.c.u-tokyo.ac.jp/~fukushima mailto:hukusima@phys.c.u-tokyo.ac.jp December 2, 2003 Today s Contents Summary 2003/12/02 1 Cannella Mydosh(1972) Edwards Anderson(1975): Model Hamiltonian:
磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論
email: takahash@sci.u-hyogo.ac.jp April 30, 2009 Outline 1. 2. 3. 4. 5. 6. 2 / 260 Today s Lecture: Itinerant Magnetism 60 / 260 Multiplets of Single Atom System HC HSO : L = i l i, S = i s i, J = L +
学位研究17号
1715 3 The Student Transfer and the Articulation System in Chinese Higher Education HUANG Meiying Research in Academic Degrees, No. 17 March, 2003the article The Journal on Academic Degrees of National
untitled
SPring-8 RFgun JASRI/SPring-8 6..7 Contents.. 3.. 5. 6. 7. 8. . 3 cavity γ E A = er 3 πε γ vb r B = v E c r c A B A ( ) F = e E + v B A A A A B dp e( v B+ E) = = m d dt dt ( γ v) dv e ( ) dt v B E v E