CLASSICAL AND QUANTUM INTEGRABILITY

被引:0
作者
Garay, Mauricio D. [1 ]
van Straten, Duco [2 ]
机构
[1] Max Planck Inst Math, D-53111 Bonn, Germany
[2] Johannes Gutenberg Univ Mainz, Inst Math, D-55099 Mainz, Germany
关键词
Micro-local analysis; non-commutative geometry; DEFORMATION QUANTIZATION; LAGRANGIAN SUBMANIFOLDS; ALGEBRAIC VARIETY; SINGULARITIES; RESOLUTION; THEOREM; FIELD;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
It is a well-known problem to decide if a classical hamiltonian system that is integrable, in the Liouville sense, can be quantised to a quantum integrable system. We identify the obstructions to do so, and show that the obstructions vanish under certain conditions.
引用
收藏
页码:519 / 545
页数:27
相关论文
共 32 条
  • [1] [Anonymous], 1955, Ann. Inst. Fourier
  • [2] [Anonymous], SEMINAIRE BOURBAKI
  • [3] [Anonymous], 1970, LECT NOTES MATH
  • [4] Arnol'd V. I., 1963, SIB MAT ZH, V4, P471
  • [5] BAYEN F, 1975, LETT MATH PHYS, V1, P521
  • [6] Quantum mechanics II
    Born, M
    Heisenberg, W
    Jordan, P
    [J]. ZEITSCHRIFT FUR PHYSIK, 1926, 35 (8/9): : 557 - 615
  • [7] Quantization of complex Lagrangian submanifolds
    D'Agnolo, Andrea
    Schapira, Pierre
    [J]. ADVANCES IN MATHEMATICS, 2007, 213 (01) : 358 - 379
  • [8] Deligne P., 1995, Selecta Math. (N.S.), V1, P667
  • [9] Dirac P A M., 1925, Proc. R. Soc. A, V109, P642, DOI [10.1098/rspa.1925.0150, DOI 10.1098/RSPA.1925.0150]
  • [10] Fedosov B., 1996, MATH TOPICS, V9