Topology of quantizable dynamical systems and the algebra of observables

Norman E. Hurt

Annales de l'I.H.P. Physique théorique (1972)

  • Volume: 16, Issue: 3, page 203-217
  • ISSN: 0246-0211

How to cite

top

Hurt, Norman E.. "Topology of quantizable dynamical systems and the algebra of observables." Annales de l'I.H.P. Physique théorique 16.3 (1972): 203-217. <http://eudml.org/doc/75735>.

@article{Hurt1972,
author = {Hurt, Norman E.},
journal = {Annales de l'I.H.P. Physique théorique},
language = {eng},
number = {3},
pages = {203-217},
publisher = {Gauthier-Villars},
title = {Topology of quantizable dynamical systems and the algebra of observables},
url = {http://eudml.org/doc/75735},
volume = {16},
year = {1972},
}

TY - JOUR
AU - Hurt, Norman E.
TI - Topology of quantizable dynamical systems and the algebra of observables
JO - Annales de l'I.H.P. Physique théorique
PY - 1972
PB - Gauthier-Villars
VL - 16
IS - 3
SP - 203
EP - 217
LA - eng
UR - http://eudml.org/doc/75735
ER -

References

top
  1. [1] J.F. Adams, On the nonexistence of elements of Hopf invariant one (Ann. of Math., vol. 72, 1960. p. 20-104). Zbl0096.17404MR141119
  2. [2] J. Adem, Relations on iterated reduced powers (Proc. Nat. Acad. Sci. U. S. A., vol. 39, 1953, p. 636-638). Zbl0052.19101MR56293
  3. [3] A.C. Allamigeon, Propriétés globales des espaces de Riemann harmoniques (Ann. Inst. Fourier, t. 15, 1965, p. 91-132). Zbl0178.55903MR198391
  4. [4] R.L. Bishop and S.I. Goldberg, Rigidity of positively curved Kähler manifolds (Proc. Nat. Acad. Sci. U. S. A., vol. 54, 1965, p. 1037-1041); On the second cohomology group of a Kähler manifold of positive sectional curvature (Proc. Amer. Math. Soc., vol. 16, 1965, p. 119-122). Zbl0129.35801MR195112
  5. [5] D.E. Blair and S.I. Goldberg, Topology of almost contact manifolds (J. Diff. Geom., vol. 1, 1967, p. 347-354). Zbl0163.43902MR226539
  6. [6] D. Bohm, B.J. Hiley and A.E.G. Stuart, Inter. J. Theor. Phys., 3, 1970, p. 171; B.J. Hiley and A.E.G. Stuart, Phase Space, Fibre bundles and current algebras (Inter. J. Theor. Phys., vol. 4, 1971, p. 247-265). MR378605
  7. [7] W.M. Boothby and H.C. Wang, On contact manifolds (Ann. of Math., vol. 68, 1968, p. 721-734). Zbl0084.39204MR112160
  8. [8] R. Bott, On manifolds all of whose geodesics are closed (Ann. of Math., 60, 1954, p. 375-382). Zbl0058.15604MR73993
  9. [9] W. Browder, Surgery and the theory of differentiable transformation groups (Proceedings of the Conference on Transformation groups) (Springer-Verlag, 1968), p. 1-46. Zbl0177.51902MR261629
  10. [10] E. Cartan, Sur les variétés à connexion projective (Bull. Soc. math. Fr., t. 52, 1924, p. 205-241). Zbl50.0500.02MR1504846JFM50.0500.02
  11. [11] P. Dazord, Variétés finslériennes à géodésiques fermées (C. R. Acad. Sc., Paris, t. 266, série A, p. 348-350; Propriétés globales des géodésiques des espaces Finsler (Thesis, 1969). Zbl0157.52304MR230266
  12. [12] J. Eells and N. Kuiper, Manifolds which are like projective planes (Public. Math. I. H. E. S., vol. 14, 1962, p. 5-46). Zbl0109.15701MR145544
  13. [13] A. Gleason, Spaces with a compact Lie group of transformations (Proc. Amer. Math. Soc., vol. 1, 1950, p. 35-43). Zbl0041.36207MR33830
  14. [14] S.I. Goldberg, Rigidity of positively curved contact manifolds (J. London Math. Soc., vol. 42, 1967, p. 257-263). Zbl0147.40802MR232325
  15. [15] S.I. Goldberg, On the topology of compact contact manifolds (Tohoku Math. J., vol. 20, 1968, p. 106-110). Zbl0174.53404MR229176
  16. [16] R.C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables (Prentice-Hall, Englewood Cliffs, 1965). Zbl0141.08601MR180696
  17. [17] M. Harada, On the curvature of Sasakian manifolds (Bull. Yamagata Univ., vol. 7, 1969, p. 97-106). MR261493
  18. [18] M. Harada, On the minimal diameter of Sasakian manifolds (Ibid., vol. 7, No. 3, 1970, p. 191-203). MR303466
  19. [19] W.C. Hsiang, A note on free differentiable actions of S1 and S3 on homotopy spheres (Ann. of Math., vol. 83, 1966, p. 266-272). Zbl0137.17802MR192506
  20. [20] W.C. Hsiang and W.Y. Hsiang, Some free differentiable actions on 11-spheres (Quart. J. Math., vol. 15, 1964, p. 371-374). Zbl0125.40201MR173266
  21. [21] S.T. Hu, Homotopy Theory (Academic Press, New York, 1959). Zbl0088.38803MR106454
  22. [22] N.E. Hurt, Remarks on Canonical Quantization (Il Nuovo Cimento, vol. 55 A, 1968, p. 534-542). Zbl0163.46501
  23. [23] N.E. Hurt, Remarks on Morse Theory in Canonical Quantization (J. Math. Phys., vol. 11, 1970, p. 539-551). MR482882
  24. [24] N.E. Hurt, Examples in Quantizable Dynamical Systems, II (Lettere al Nuovo Cimento, vol. 3, 1970, p. 137-138). 
  25. [25] N.E. Hurt, Differential Geometry of Canonical Quantization (Ann. Inst. H. Poincaré, vol. XIV, No.2, 1971, p. 153-170). Zbl0211.54003MR296982
  26. 26] N.E. Hurt, A classification theory of quantizable dynamical systems (Report on Math. Phys., vol. 2, 1971, p. 211-220). Zbl0224.53021MR322902
  27. [27] M. Kervaire, A manifold which does not admit any differentiable structure (Comm. Math. Helv., vol. 34, 1960, p. 257-270). Zbl0145.20304MR139172
  28. [28] M. Kervaire and J.W. Milnor, Groups of Homotopy Spheres, I (Ann. of Math., vol. 77, 1963), p. 504-537). Zbl0115.40505MR148075
  29. [29] W. Klingenberg, Manifolds with restricted conjugate locus (Ann. of Math., vol. 78, 1963, p. 527-547). Zbl0117.38701MR159289
  30. [30] K. Kodaira, On Kähler varieties of restricted type (Ann. of Math., vol., 60, 1954, p. 28-48). Zbl0057.14102MR68871
  31. [31] R. Lee, Nonexistence of Free differentiable actions of S1 and Z2 on Homotopy spheres, [9], p. 208-209. Zbl0172.48401MR245040
  32. [32] G. Mackey, Mathematical Foundations of Quantum Mechanics (Benjamin, New York, 1963). Zbl0114.44002
  33. [33] J. Milnor, On manifolds homeomorphic to the 7-sphere (Ann. of Math., vol. 64, 1956, p. 399-405). Zbl0072.18402MR82103
  34. [34] J. Milnor, On the existence of a connection with curvature zero (Comm. Math. Helv., vol. 32, 1957, p. 215-223). Zbl0196.25101MR95518
  35. [35] C.W. Misner and J.A. Wheeler, Gravitation, Electromagnetism Unquantized Charge, and Mass as properties of curved empty space (Ann. of Phys., vol. 2, 1957, p. 525-660). Zbl0078.19106MR93387
  36. [36] D. Montgomery and C.T. Yang, Differentiable Actions on homotopy seven sphere, I (Trans Amer. Math. Soc., vol. 122, 1966, p. 480-498). Zbl0138.18703MR200934
  37. [37] D. Montgomery and C.T. Yang, Differentiable Actions on homotopy seven sphere, II, [9], p. 125-133. Zbl0177.51903MR245041
  38. [38] J.R. Munkres, Obstructions to smoothing a piecewise differentiable homeomorphism (Ann. of Math., vol. 72, 1960, p. 521-554). Zbl0108.18101MR121804
  39. [39] J.R. Munkres, Elementary Differential Topology (Princeton University Press, 1966). Zbl0161.20201MR198479
  40. [40] H. Nakagawa, A note on theorems of Bott and Samelson (J. Math. of Kyoto Univ., vol., 7, 1967, p. 205-220); Riemannian manifolds with many geodesic loops (J. Math. Soc. Japan, vol. 20, 1968, p. 648-654). Zbl0162.53502MR225339
  41. [41] G. Reeb, Sur certaines propriétés topologiques des trajectoires des systèmes dynamiques (Mém. Acad. roy. Belgique, Cl. Sc., vol. 27, n° 9, 1952, p. 1-64). Zbl0048.32903MR58202
  42. [42] G. Reeb, Trois problèmes de la théory des systèmes dynamique, (Colloq. Géom. Diff. Global) (C. B. R. M., 1958), p. 89-94. Zbl0095.29002MR121808
  43. [43] H. Samelson, On manifolds with many closed geodesics (Portugaliae Math., vol. 22, 1963, p. 193-196). Zbl0134.17704MR230256
  44. [44] S. Smale, Generalized Poincaré conjecture in dimensions greater than four (Ann. of Math., vol. 74, 1961, p. 391-406). Zbl0099.39202MR137124
  45. [45] S. Smale, Stable manifolds for differential equations and diffeomorphisms (Ann. Scola Normu. Sup. Pisa, vol. 17, 1963, p. 97-116). Zbl0113.29702MR165537
  46. [46] J.M. Souriau, Structure des systèmes dynamiques (Dunod, Paris, 1970). Zbl0186.58001MR260238
  47. [47] E. Spainier, Algebraic Topology (Mc Craw-Hill, New York, 1966). Zbl0145.43303
  48. [48] J. Stallings, The piecewise-linear structure of euclidean space (Proc. Cambridge Phil. Soc., vol. 58, 1962, p. 481-488). Zbl0107.40203MR149457
  49. [49] N. Steenrod, The Topology of Fiber Bundles (Princeton University Press, Princeton, 1951). Zbl0054.07103
  50. [50] S. Tanno, The topology of contact Riemannian manifolds (Ill. J. Math., vol. 12, 1968, p. 700-717). Zbl0165.24703MR234486
  51. [51] H.O. Singh Varma, Homogeneous manifolds all of whose geodesics are closed (Indag. Math., vol. 48, 1965, p. 813-819). Zbl0135.40501MR190949

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.