Quantization of the cotangent bundle via the tangent groupoid

• Autorzy: José F. Cariñena , Jesús Clemente-Gallardo
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2000
• Tom: 51
• Numer: 1
• Strony: 43-53

Daty

wydano

2000

Twórcy

autor

José F. Cariñena

• Departamento de Física Teórica, Universidad de Zaragoza, 50009, Zaragoza, Spain

autor

Jesús Clemente-Gallardo

• Departamento de Física Teórica, Universidad de Zaragoza, 50009, Zaragoza, Spain

Bibliografia

• [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.
• [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.
• [3] J. Clemente-Gallardo, Ph. D Thesis, University of Zaragoza, 1999.
• [4] A. Connes, Noncommutative Geometry, Academic Press, London, 1994.
• [5] A. Connes and Hilson, Déformations, morphismes asymptotiques et K-théorie bivariante, C. R. Acad. Sci. Paris 311, Sér. I, 101-106.
• [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.
• [7] B. Fedosov, Deformation quantization and index theory, Akademie Verlag, 1996.
• [8] M. J. Gotay, Obstructions to quantization, preprint math-ph/9809011; The Juan Simo Memorial Volume, J. Marsden and S. Wiggins (eds.), Springer, 1998.
• [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.
• [10] N. P. Landsman, Strict deformation quantization of a particle in external gravitational and Yang-Mills fields, J. Geom. Phys. 12 (1993), 93-132.
• [11] S. Lang, Differential Manifolds, Addison-Wesley, Reading, Mass., 1972.
• [12] B. Monthubert and F. Pierrot, Indice analytique et groupoïdes de Lie, C. R. Acad. Sci. Paris 325 (1997), 193-198.
• [13] M. Rieffel, Questions on quantization, preprint quant-ph/9712009; Proc. Internat. Conf. on Operator Algebras and Operator Theory (Shanghai, 1997).