Supersymmetric noncommutative geometry and quantum physics

2008 Fiscal Year Final Research Report

• Project/Area Number: 18540380
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Osaka Prefecture University
• Principal Investigator: AIZAWA Naruhiko Osaka Prefecture University, 理学系研究科, 准教授 (70264786)
• Co-Investigator(Renkei-kenkyūsha): CHAKRABARTI Ranabir Department of Theoretical Physics, University of Madras, Reader ; SEGAR Jambulingam Department of Physics, Ramakrishna Mission Vivekananda College, Lecturer-SS
• Project Period (FY): 2006 – 2008
• Keywords: 量子群 / 表現論 / 非可換幾何学 / 特殊関数

Research Abstract

我々の住んでいる時空は本当に連続的なものなのか?という疑問は1940年代から存在する。近年、座標(x, y)が非可換量、すなわちxy≠yxであるような対象が物理の中で重要性を増してきた。近代の物理学において重要なもうひとつの概念は超対称性である。この研究では超対称性と非可換な空間を結びつけた理論を、主に量子群と呼ばれる数学的対象を用いて展開した。いくつかの量子群で具体的な計算を行ったところ、量子群の数学的性質を正確に取り込むことにより、物理学でなじみのある概念や関係式を自然な形で非可換な世界へ拡張できることを示した。

Research Products

• [Journal Article] Rerpesentations of fuzzy torus (2008)
  • Author(s): N. Aizawa and R. Chakrabarti
  • Journal Title: Journal of Physics : Conference Series Vol.128 Pages: 012047(14)
  • Peer Reviewed
• [Journal Article] Representations of quantum supergroups and basic hypergeometric functions (2007)
  • Author(s): N. Aizawa, R. Chakrabarti, S.S. Naina Mohammed and J. Segar
  • Journal Title: Publicaciones de la Real Sociedad Matematica Espanola Vol.11 Pages: 210-215
  • Peer Reviewed
• [Journal Article] Fuzzy torus via q-parafermion (2007)
  • Author(s): N. Aizawa and R. Chakrabarti
  • Journal Title: Journal of Physics A : Mathematical and Theoretical Vol.40 Pages: 10021-10030
  • Peer Reviewed
• [Journal Article] Basic hypergeometric functions and covariant spaces for even dimensional representations of Uq[osp(1/2)] (2007)
  • Author(s): N. Aizawa, R. Chakrabarti, S.S. Naina Mohammed and J. Segar
  • Journal Title: Journal of Physics A : Mathematical and Theoretical Vol.40 Pages: 14985-15000
  • Peer Reviewed
• [Journal Article] Otsuki, All link invariants for two dimensional solutions of Yang-Baxter equation and dressings (2006)
  • Author(s): N. Aizawa, M. Harada, M. Kawaguchi and E
  • Journal Title: Journal of Knot Theory and Its Ramifications Vol.15 Pages: 1279-1301
  • Peer Reviewed
• [Journal Article] Universal T-marix, representations of OSpq(1/2) and little Q-Jacobi polynomials (2006)
  • Author(s): N. Aizawa, R. Chakrabarti, S.S. Naina Mohammed and J. Segar
  • Journal Title: Journal of Mathematical Physics Vol.47 Pages: 123511
  • Peer Reviewed
• [Journal Article] Coherent state on SUq(2) homo- geneous space
  • Author(s): N. Aizawa and R. Chakrabarti
  • Journal Title: Journal of Physics A : Mathematical and Theoretical (掲載決定)
  • Peer Reviewed
• [Presentation] Coherent state による量子群の等質空間の非可換性 (2009)
  • Author(s): 會澤成彦
  • Organizer: 日本物理学会
  • Place of Presentation: 立教大学
  • Year and Date: 2009-03-30
• [Presentation] Noncommutative structure of quantum group coherent states (2009)
  • Author(s): 會澤成彦
  • Organizer: 3rd International Meeting on Frontiers of Physics
  • Place of Presentation: Genting highlands, Malaysia
  • Year and Date: 2009-01-14
• [Presentation] SUq(2) coherent state と非可換球面 (2008)
  • Author(s): 會澤成彦
  • Organizer: 日本数学会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-25
• [Presentation] 非可換な coherent state とその性質 (2008)
  • Author(s): 會澤成彦
  • Organizer: 日本物理学会
  • Place of Presentation: 岩手大学
  • Year and Date: 2008-09-22
• [Presentation] Noncommutative coherent states for quantum groups (2008)
  • Author(s): 會澤成彦
  • Organizer: Noncommutative Structures in Mathematics and Physics
  • Place of Presentation: Brussels, Belgium
  • Year and Date: 2008-07-23
• [Presentation] ファジィトーラスの行列表示と非可換幾何学 (2007)
  • Author(s): 會澤成彦
  • Organizer: 日本物理学
  • Place of Presentation: 北海道大学
  • Year and Date: 2007-09-22
• [Presentation] Representations of fuzzy torus (2007)
  • Author(s): 會澤成彦
  • Organizer: 5th International Symposium "Quantum Theory and Symmetries"
  • Place of Presentation: Valladolid, Spain
  • Year and Date: 2007-07-23
• [Presentation] Quantum supergroupと特殊関数 (2006)
  • Author(s): 會澤成彦
  • Organizer: 日本物理学会
  • Place of Presentation: 千葉大学
  • Year and Date: 2006-09-24
• [Presentation] OSpq(1/2)の表現とQ-hypergeometric functions (2006)
  • Author(s): 會澤成彦
  • Organizer: 日本数学会
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2006-09-19
• [Remarks] N. Aizawa and R. Chakrabarti, Noncommutative superspaces covariant under OSpq(1/2) algebra, in "Proceedings of the VI International Workshop on Lie Theory and Its Applications in Physics", H.-D. Doebner and V. K. Dobrev (editor), Heron Press (Sofia)(2006) 97-108
• [Remarks] N. Aizawa, V. K. Dobrev, H.-D. Doebner and S. Stoimenov, Intertwinig operators for the Schrodinger algebra in n≧3 space dimension, in "Proceedings of the VII International Workshop on Lie Theory and Its Applications in Physics", H.-D. Doebner and V. K. Dobrev (editor), Heron Press (Sofia)(2008) 372-399