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小竹 悟  オダケ サトル

教員組織学術研究院(理学系)電話番号
教育組織理学部 理学科 物理学コースFAX番号
職名教授メールアドレス
住所〒390-8621 長野県松本市旭3-1-1ホームページURLhttp://azusa.shinshu-u.ac.jp/~odake/index.html

更新日:2017/06/30

プロフィール

兼担研究科・学部
大学院理工学系研究科 (修士課程) 物質基礎科学専攻
大学院総合工学系研究科 (博士課程) 物質創成科学専攻 物質解析科学講座
COE・クラスタ・
研究グループ
素粒子理論研究室
研究分野
素粒子
数理物理
現在の研究課題
素粒子理論・数理物理学(弦理論、共形場理論、無限次元代数、可積分系)

自然界の根幹をなす素粒子論の究極の統一理論の候補である弦理論や、共形変換の下で不変な理論である共形場理論(弦理論や統計臨界系が含まれる)や、様々な可積分系を研究してきた。最近は解ける量子力学模型の研究を行っている。

所属学会
所属学会
日本物理学会

所属学会役職担当
1999-2000 , 日本物理学会 , 素粒子論分科会世話人
学歴
出身大学院
1989 , 東京大学 , 理学系研究科 , 物理学専門課程
1986 , 東京大学 , 理学系研究科 , 物理学専門課程

出身学校・専攻等(大学院を除く)
1984 , 東京大学 , 理学部 , 物理学科

取得学位
理学博士 , 東京大学
研究職歴等
研究職歴
2006- , 信州大学 理学部 教授
1997-2006 , 信州大学 理学部 助教授
1995-1997 , 信州大学 理学部 講師
1993-1995 , 信州大学 教養部 講師
1992-1993 , 素粒子奨学会 奨学生
1991-1992 , 湯川紀年財団 奨学研究員
1989-1991 , 日本学術振興会 特別研究員

研究活動業績

研究業績(著書・
発表論文等)
著書
ストリング理論 第2巻
シュプリンガー・フェアラーク東京 2006
Author:伊藤 克司,小竹 悟,松尾 泰


ストリング理論 第1巻
シュプリンガー・フェアラーク東京 2005
Author:伊藤 克司,小竹 悟,松尾 泰


論文
New Determinant Expressions of the Multi-indexed Orthogonal Polynomials in Discrete Quantum Mechanics
Progress of Theoretical and Experimental Physics,2017(5):053A01 2017
Author:S.Odake


Simplified Expressions of the Multi-indexed Laguerre and Jacobi Polynomials
SIGMA,13:020 2017
Author:S.Odake and R.Sasaki


Multi-indexed Meixner and Little q-Jacobi (Laguerre) Polynomials
Journal of Physics,50(16):165204 2016
Author:S.Odake and R.Sasaki


Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators
Journal of Mathematical Physics,57(11):113503 2016
Author:S.Odake


Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III
Journal of Mathematical Physics,57(2):023514 2016
Author:S.Odake


Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm
Journal of Mathematical Physics,56(7):073502 2015
Author:S.Odake and R.Sasaki


Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II
Journal of Mathematical Physics,56(5):053506 2015
Author:S.Odake


Reflectionless Potentials for Difference Schr\"odinger Equations
Journal of Physics,A48(11):115204 2015
Author:S.Odake and R.Sasaki


Casoratian Identities for the Wilson and Askey-Wilson Polynomials
Journal of Approximation Theory,193:184-209 2015
Author:S.Odake and R.Sasaki


Equivalences of the multi-indexed orthogonal polynomials
Journal of Mathematical Physics,55:013502 2014
Author:S.Odake


Non-polynomial extensions of solvable potentials a la Abraham-Moses
Journal of Mathematical Physics,54:102106 2013
Author:S.Odake and R.Sasaki


Recurrence Relations of the Multi-Indexed Orthogonal Polynomials
Journal of Mathematical Physics,54:083506 2013
Author:S.Odake


Extensions of solvable potentials with finitely many discrete eigenstates
Journal of Physics,A46:235205 2013
Author:S.Odake and R.Sasaki


Krein-Adler transformations for shape-invariant potentials and pseudo virtual states
Journal of Physics,A46:245201 2013
Author:S.Odake and R.Sasaki


Multi-indexed Wilson and Askey-Wilson Polynomials
Journal of Physics,A46:045204 2013
Author:S.Odake and R.Sasaki


Multi-indexed (q-)Racah Polynomials
Journal of Physics,A45:385201 2012
Author:S.Odake and R.Sasaki


Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
Physics Letters,B702:164 2011
Author:S.Odake and R.Sasaki


Discrete Quantum Mechanics
Journal of Physics,A44:353001 2011
Author:S.Odake and R.Sasaki


The Exceptional (X_{\ell}) (q)-Racah Polynomials
Progress of Theoretical Physics,125(5):851 2011
Author:S.Odake and R.Sasaki


Dual Christoffel transformations
Progress of Theoretical Physics,126:1 2011
Author:S.Odake and R.Sasaki


A new family of shape invariantly deformed Darboux-P\"oschl-Teller potentials with continuous \ell
Journal of Physics,A44:195203 2011
Author:S.Odake and R.Sasaki


Properties of the exceptional (X-l) Laguerre and Jacobi polynomials
SIGMA,7:107 2011
Author:C.-L.Ho, S.Odake and R.Sasaki


Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations
Journal of Physics,A43:335201 2010
Author:S.Odake and R.Sasaki


Modification of Crum's Theorem for `Discrete' Quantum Mechanics
Progress of Theoretical Physics,124(1):1-26 2010
Author:L..Garcia-Gutierrez, S.Odake and R.Sasaki


Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism
Journal of Mathematical Physics,51:083502 2010
Author:S.Odake and R.Sasaki


Another set of infinitely many exceptional ($X_{\ell}$) Laguerre polynomials
Physics Letters,B684:173-176 2010
Author:S.Odake and R.Sasaki


Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
Journal of Mathematical Physics,51:053513 2010
Author:S.Odake and R.Sasaki


Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials
Physics Letters,B682:130 2009
Author:S.Odake and R.Sasaki


Infinitely many shape invariant potentials and new orthogonal polynomials
Physics Letters,B679:414 2009
Author:S.Odake and R.Sasaki


Crum's Theorem for `Discrete' Quantum Mechanics
Progress of Theoretical Physics,122(5):1067-1079 2009
Author:S.Odake and R.Sasaki


Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states
Progress of Theoretical Physics,119(4):663-700 2008
Author:S.Odake and R.Sasaki


Orthogonal Polynomials from Hermitian Matrices
Journal of Mathematical Physics,49(5):053503 2008
Author:S.Odake and R.Sasaki


q-oscillator from the q-Hermite Polynomial
Physics Letters,B663(1-2):141-145 2008
Author:S.Odake and R.Sasaki


Multi-Particle Quasi Exactly Solvable Difference Equations
Journal of Mathematical Physics,48(12):122105 2007
Author:S.Odake and R.Sasaki


Interpolation of SUSY quantum mechanics
Journal of Physics,A40(39):11973-11986 2007
Author:S.Odake, Y.Pehlivan and R.Sasaki


Exact Heisenberg operator solutions for multi-particle quantum mechanics
Journal of Mathematical Physics,48(8):082106 2007
Author:S.Odake and R.Sasaki


Exact solution in the Heisenberg picture and annihilation-creation operators
Physics Letters,B641(1):112-117 2006
Author:S.Odake and R.Sasaki


Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
Journal of Mathematical Physics,47(10):102102 (33pages) 2006
Author:S.Odake and R.Sasaki


Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics
Rokko Lectures in Mathematics (Kobe University) (Elliptic Integrable Systems, Eds. M.Noumi and K.Takasaki),18:85-110 2005
Author:S.Odake and R.Sasaki


Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials
Progress of Theoretical Physics,114(6):1245-1260 2005
Author:S.Odake and R.Sasaki


Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials
Journal of Mathematical Physics,46(6):063513 (10pages) 2005
Author:S.Odake and R.Sasaki


Shape Invariant Potentials in ``Discrete Quantum Mechanics"
Journal of Nonlinear Mathematical Physics,12 Supplement 1:507-521 2005
Author:S.Odake and R.Sasaki


Polynomials Associated with Equilibria of Affine Toda-Sutherland Systems
Journal of Physics,A37(47):11401-11406 2004
Author:S.Odake and R.Sasaki


Equilibria of `Discrete' Integrable Systems and Deformations of Classical Orthogonal Polynomials
Journal of Physics,A37(49):11841-11876 2004
Author:S.Odake and R.Sasaki


Virasoro-type Symmetries in Solvable Models
Proceedings of the Canada-China Meeting on Theoretical Physics edited by L.Lapointe, M.-L.Ge, Y.Saint-Aubin and L.Vinet,:154-188 2003
Author:H.Awata, H.Kubo, S.Odake and J.Shiraishi


Quantum Deformation of the W_N Algebra
Proceedings of the Canada-China Meeting on Theoretical Physics edited by L.Lapointe, M.-L.Ge, Y.Saint-Aubin and L.Vinet,:112-130 2003
Author:H.Awata, H.Kubo, S.Odake and J.Shiraishi


Polynomials Associated with Equilibrium Positions in Calogero-Moser Systems
Journal of Physics,A35(39):8283-8314 2002
Author:S.Odake and R.Sasaki


Comments on the deformed W-N algebra
INTERNATIONAL JOURNAL OF MODERN PHYSICS B,16(14-15):2055-2064 2002
Author:S.Odake


On Lepowsky-Wilson's {\cal Z}-algebra
Contemporary Mathematics,297:143-149 2002
Author:Y.Hara, M.Jimbo, H.Konno, S.Odake and J.Shiraishi


Beyond CFT : Deformed Virasoro and Elliptic Algebras
`Theoretical Physics at the End of the Twentieth Century' (Lecture Notes of the CRM Summer School, Banff, Alberta) edited by Y.Saint-Aubin and L.Vinet,:307-449 2002
Author:S.Odake


Free Field Construction for the ABF Models in Regime II
Journal of Statistical Physics,102(3-4):883-921 2001
Author:M.Jimbo, H.Konno, S.Odake, Y.Pugai and J.Shiraishi


Quasi-Hopf twistors for elliptic quantum groups
`Yang-Baxter Systems, Nonlinear Models and Their Applications' edited by B.K. Chung, Q-Han Park and C.Rim,:173-182 2000
Author:S.Odake


Free Field Approach to the Dilute A_L Models
Journal of Mathematical Physics,40:3791-3826 1999
Author:Y.Hara, M.Jimbo, H.Konno, S.Odake and J.Shiraishi


Elliptic algebra U_{q,p}(\widehat{sl}_2) : Drinfeld currents and vertex operators
Communications in Mathematical Physics,199:605-647 1999
Author:M.Jimbo, H.Konno, S.Odake and J.Shiraishi


Quasi-Hopf twistors for elliptic quantum groups
Transformation Groups,4:303-327 1999
Author:M.Jimbo, H.Konno, S.Odake and J.Shiraishi


共形場理論を越えて -- 変形 Virasoro 代数が開く扉 --
日本物理学会誌,53(3):170-180 1998
Author:粟田 英資, 久保 晴信, 守田 佳史, 小竹 悟, 白石 潤一


q-Difference Realization of U_q(sl(M|N)) and Its Application to Free Boson Realization of U_q(\widehat{sl}(2|1))
Letters in Mathematical Physics,42:271-279 1997
Author:H.Awata, S.Odake and J.Shiraishi


Vertex Operators of the q-Virasoro Algebra; Defining Relations, Adjoint Actions and Four Point Functions
Letters in Mathematical Physics,41:65-78 1997
Author:H.Awata, H.Kubo, Y.Morita, S.Odake and J.Shiraishi


Reflection K-Matrices of the 19-Vertex Model and XXZ Spin-1 Chain with General Boundary Terms
Nuclear Physics,B470[FS]:419-432 1996
Author:T.Inami, S.Odake and Y-Z.Zhang


Quantum {\cal W}_N Algebras and Macdonald Polynomials
Communications in Mathematical Physics,179:401-416 1996
Author:H.Awata, H.Kubo, S.Odake and J.Shiraishi


A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
Letters in Mathematical Physics,38:33-51 1996
Author:J.Shiraishi, H.Kubo, H.Awata and S.Odake


Integral Representations of the Macdonald Symmetric Polynomials
Communications in Mathematical Physics,179:647-666 1996
Author:H.Awata, S.Odake and J.Shiraishi


Supersymmetric Extension of the Sine-Gordon Theory with Integrable Boundary Interaction
Physics Letters,B359:118-124 1995
Author:T.Inami, S.Odake and Y-Z.Zhang


A Note on Calogero-Sutherland Model, W_n Singular Vectors and Generalized Matrix Models
Soryushiron Kenkyu(Kyoto),91:A69-A75 1995
Author:H.Awata, Y.Matsuo, S.Odake and J.Shiraishi


Excited States of Calogero-Sutherland Model and Singular Vectors of the W_N Algebra
Nuclear Physics,B449:347-374 1995
Author:H.Awata, Y.Matsuo, S.Odake and J.Shiraishi


Collective Field Theory, Calogero--Sutherland Model and Generalized Matrix Models
Physics Letters,B347:49-55 1995
Author:H.Awata, Y.Matsuo, S.Odake and J.Shiraishi


Representation Theory of $W_{1+\infty}$ algebra
`Group Theoretical Methods in Physics' edited by A.Arima, T.Eguchi and N. Nakanishi,:335-338 1995
Author:H.Awata, M.Fukuma, Y.Matsuo and S.Odake


Representation Theory of The W_{1+\infty} Algebra
Progress of Theoretical Physics Proceedings Supplement,118:343-373 1995
Author:H.Awata, M.Fukuma, Y.Matsuo and S.Odake


Subalgebras of $W_{1+\infty}$ and Their Quasifinite Representations
Journal of Physics,A28:105-112 1995
Author:H.Awata, M.Fukuma, Y.Matsuo and S.Odake


Character and Determinant Formulae of Quasifinite Representation of the W_{1+\infty} Algebra
Communications in Mathematical Physics,172:377-400 1995
Author:H.Awata, M.Fukuma, Y.Matsuo and S.Odake


Quasifinite Highest Weight Modules over Super W_{1+\infty} Algebra
Communications in Mathematical Physics,170:151-179 1995
Author:H.Awata, M.Fukuma, Y.Matsuo and S.Odake


場の理論的方法によるスピン鎖
物性研究,61:648-653 1994
Author:小竹 悟


Determinant Formulae of Quasi-Finite Representation of W_{1+\infty} Algebra at Lower Levels
Physics Letters,B332:336-344 1994
Author:H.Awata, M.Fukuma, Y.Matsuo and S.Odake


Eigensystem and Full Character Formula of the {\cal W}_{1+\infty} Algebra with c=1
Letters in Mathematical Physics,31:289-298 1994
Author:H.Awata, M.Fukuma, S.Odake and Y.-H.Quano


Heisenberg realization for U_q(sl_n) on the flag manifold
Letters in Mathematical Physics,30:35-43 1994
Author:H.Awata, M.Noumi and S.Odake


Free Boson Realization of U_q(\widehat{sl}_N)
Communications in Mathematical Physics,162:61-83 1994
Author:H.Awata, S.Odake and J.Shiraishi


Free Boson Representation of U_q(\widehat{sl}_3)
Letters in Mathematical Physics,30:207-216 1994
Author:H.Awata, S.Odake and J.Shiraishi


Field Theory Limit of Spin-1 Chain
`Current Topics in Theoretical Physics' edited by Y.M.Cho,:113-124 1994
Author:T.Inami and S.Odake


スピン1XXZ鎖の連続極限
素粒子論研究,87:107-119 1993
Author:小竹 悟


Continuum Limit of Spin-1 Chain
Physical Review Letters,70:2016-2019 1993
Author:T.Inami and S.Odake


W 無限大代数のユニタリ表現
素粒子論研究,85:237-254 1992
Author:小竹 悟


Unitary Representations of $W$ Infinity Algebras
International Journal of Modern Physics,A7:6339-6355 1992
Author:S.Odake


Two Matrix Model and Minimal Unitary Model
Physics Letters,B269:300-304 1991
Author:S.Odake


Comments on the $W_{1+\infty}$ and Super $W_{\infty}$ Algebras with $SU(N)$ Symmetry
KEK Proceedings,91-6:80-94 1991
Author:S.Odake and T.Sano


W_{1+\infty} and Super W_{\infty} Algebras with SU(N) Symmetry
Physics Letters,B258:369-374 1991
Author:S.Odake and T.Sano


Nonperturbative Analysis of Three Matrix Model
Physics Letters,B247:57-63 1990
Author:H.Kunitomo and S.Odake


c=3d Algebra
Proceedings of the Workshop ``Topology, Field Theory and Superstring" KEK report ,89-22:133-142 1990
Author:S.Odake


c=3d Conformal Algebra with Extended Supersymmetry
Modern Physics Letters,A5:561-580 1990
Author:S.Odake


Character Formulas of an Extended Superconformal Algebra Relevant to String Compactification
International Journal of Modern Physics,A5:897-914 1990
Author:S.Odake


超共形代数とその拡張について
素粒子論研究,78:201-260 1989
Author:小竹 悟


Extension of N=2 Superconformal Algebra and Calabi-Yau Compactification
Modern Physics Letters,A4:557-568 1989
Author:S.Odake


Operator Product Expansion Coefficients in N=1 Superconformal Theory and Slightly Relevant Perturbation
Nuclear Physics,B306:425-444 1988
Author:Y.Kitazawa, N.Ishibashi, A.Kato, K.Kobayashi, Y.Matsuo and S.Odake


Fermionic Construction of N=0,1,2 (Super)Conformal Algebras
Proceedings of 7th INS Winter Seminar on Superstrings, Composite Models and Anomaly Related Problems,:199-211 1988
Author:K.Kobayashi and S.Odake


Fermionic Construction of N=0,1,2 (Super)Conformal Algebras
Modern Physics Letters,A3:773-781 1988
Author:K.Kobayashi and S.Odake


Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude
素粒子論研究,75:E3-E5 1987
Author:加藤 晃史,松尾 泰,小竹 悟


Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude
Physics Letters,B179:241-246 1986
Author:A.Kato, Y.Matsuo and S.Odake

教育活動実績

授業等
2017 , 前期 , 物理数学II
2017 , 前期 , 力学III
2017 , 前期 , 物理と対称性
2017 , 前期 , 物理学演習Ⅰ(一部分)
2017 , 前期 , 物理学演習Ⅳ(半分)
2017 , 後期 , 物理数学I
2017 , 後期 , 物理数学III
2017 , 後期 , 物理学最前線(一部分)
2017 , 後期 , 物理学演習Ⅱ(一部分)
2017 , 後期 , アドバンス演習実験実習Ⅱ(一部分)
2017 , 後期 , 先端科学特別講義(一部分)
2017 , 通年 , 物質基礎科学セミナー
2016 , 前期 , 物理数学II
2016 , 前期 , 力学III
2016 , 前期 , 物理と対称性
2016 , 前期 , 物理学演習Ⅰ(一部分)
2016 , 前期 , 物理学演習Ⅳ(半分)
2016 , 後期 , 物理数学I
2016 , 後期 , 物理数学III
2016 , 後期 , 物理学最前線(一部分)
2016 , 後期 , 物理学演習Ⅱ(一部分)
2016 , 後期 , アドバンス演習実験実習Ⅱ(一部分)
2016 , 後期 , 先端科学特別講義(一部分)
2016 , 通年 , 物質基礎科学セミナー
2015 , 前期 , 物理数学II
2015 , 前期 , 力学III
2015 , 前期 , 力学
2015 , 前期 , 物理と対称性
2015 , 前期 , 物理学演習Ⅰ(一部分)
2015 , 前期 , 新入生ゼミナール
2015 , 前期 , 宇宙物理学(一部分)
2015 , 後期 , 物理数学I
2015 , 後期 , 物理数学III
2015 , 後期 , 物理学最前線(一部分)
2015 , 後期 , 物理学演習Ⅱ(一部分)
2015 , 後期 , アドバンスゼミ(一部分)
2015 , 通年 , 物質基礎科学セミナー