Quantization of the cotangent bundle via the tangent groupoid
Cariñena, José ; Clemente-Gallardo, Jesús
Banach Center Publications, Tome 51 (2000), p. 43-53 / Harvested from The Polish Digital Mathematics Library
Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:209042
@article{bwmeta1.element.bwnjournal-article-bcpv51z1p43bwm,
     author = {Cari\~nena, Jos\'e and Clemente-Gallardo, Jes\'us},
     title = {Quantization of the cotangent bundle via the tangent groupoid},
     journal = {Banach Center Publications},
     volume = {51},
     year = {2000},
     pages = {43-53},
     zbl = {0987.53035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p43bwm}
}
Cariñena, José; Clemente-Gallardo, Jesús. Quantization of the cotangent bundle via the tangent groupoid. Banach Center Publications, Tome 51 (2000) pp. 43-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p43bwm/

[000] [1] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization, I and II. Annals of Physics 111 (1978), 61-110 and 111 (1978), 111-151. | Zbl 0377.53024

[001] [2] J. F. Cariñena, J. Clemente-Gallardo, E. Follana, J. M. Gracia-Bondía, A. Rivero and J. C. Varilly, Connes' tangent groupoid and strict quantization, J. Geom. Phys. 32 (1999), 79-96. | Zbl 0961.53047

[002] [3] J. Clemente-Gallardo, Ph. D Thesis, University of Zaragoza, 1999.

[003] [4] A. Connes, Noncommutative Geometry, Academic Press, London, 1994.

[004] [5] A. Connes and Hilson, Déformations, morphismes asymptotiques et K-théorie bivariante, C. R. Acad. Sci. Paris 311, Sér. I, 101-106.

[005] [6] M. De Wilde and P. B. Lecomte. Existence of star products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds. Lett. Math. Phys. 7 (1983), 487-496. | Zbl 0526.58023

[006] [7] B. Fedosov, Deformation quantization and index theory, Akademie Verlag, 1996.

[007] [8] M. J. Gotay, Obstructions to quantization, preprint math-ph/9809011; The Juan Simo Memorial Volume, J. Marsden and S. Wiggins (eds.), Springer, 1998.

[008] [9] M. Hilsum and G. Skandalis, Morphismes K-orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov, Ann. Sci. Ec. Norm. Sup. 20 (1987), 325-390. | Zbl 0656.57015

[009] [10] N. P. Landsman, Strict deformation quantization of a particle in external gravitational and Yang-Mills fields, J. Geom. Phys. 12 (1993), 93-132. | Zbl 0789.58081

[010] [11] S. Lang, Differential Manifolds, Addison-Wesley, Reading, Mass., 1972.

[011] [12] B. Monthubert and F. Pierrot, Indice analytique et groupoïdes de Lie, C. R. Acad. Sci. Paris 325 (1997), 193-198. | Zbl 0955.22004

[012] [13] M. Rieffel, Questions on quantization, preprint quant-ph/9712009; Proc. Internat. Conf. on Operator Algebras and Operator Theory (Shanghai, 1997).