Abstract
We use star representation geometric methods to obtain explicit oscillatory integral formulae for strongly invariant star products on Iwasawa subgroups AN of SU(1,n)
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D. Arnal J.-C. Cortet (1985) ArticleTitle*-products in the method of orbits for nilpotent groups J. Geom. Phys. 2 83–116
Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A. and Sternheimer, D.: Deformation theory and quantization. I. Deformations of symplectic structures, Ann. Phys. 111 (1978), 61–110.
Bieliavsky, P.: Semi-simple symplectic symmetric spaces, Geom. Dedicata 73(3) (1998), 245–273.
Bieliavsky, P.: Strict quantization of solvable symmetric spaces, math.QA/0010004.
Cattaneo, A. S. and Felder, G.: A path integral approach to the Kontsevich quantization formula, math.QA/9902090.
Fronsdal, C.: Some ideas about quantization, Rep. Math. Phys. 15(1) (1979), 111–145.
Hansen, F.: Quantum mechanics in phase space, Rep. Math. Phys. 19 (1984), 361–381.
Helgason, S.: Differential Geometry, Lie Groups and Symmetric Spaces, Pure Appl. Math. 80, Academic Press, New York, 1978.
Koh, S.: On affine symmetric spaces, Trans. Amer. Math. Soc. 119 (1965), 291–309.
Lichnerowicz, A. and Medina, A.: Groupes à structures symplectiques ou kaehleriennes invariantes, C.R. Acad. Sci. Paris Ser. I 306(3) (1988), 133–138.
Pedersen, N. V.: On the symplectic structure of coadjoint orbits of (solvable) Lie groups and applications. I, Math. Ann. 281(4) (1988), 633–669.
Rieffel, M. A.: Deformation quantization for actions of R d, Mem. Amer. Math. Soc. 106 (1993), No. 506.
Sternheimer, D.: Deformation quantization: Twenty years after, In: Particles, Fields, and Gravitation (Lodz, 1998), AIP Conf. Proc. 453, Amer. Inst. Phys., Woodbury, NY, 1998, pp. 107–145. math.QA/9809056.
Unterberger, A.: Quantization, symmetries and relativity, In: Lewis A. Coburn et al. (eds), Perspectives on Quantization. Proc. AMS-IMS-SIAM joint summer reseach conference, Mt. Holyoke College, South Hadley, MA, 1996, Contemp. Math. 214, Amer. Math. Soc., Providence, RI, 1998, pp. 169–187.
Weinstein, A.: Traces and triangles in symmetric symplectic spaces, In: Symplectic Geometry and Quantization (Sanda and Yokohama, 1993), Contemp. Math. 179, Amer. Math. Soc., Providence, RI, 1994, pp. 261–270.
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Bieliavsky, P., Massar, M. Oscillatory Integral Formulae for Left-invariant Star Products on a Class of Lie Groups. Letters in Mathematical Physics 58, 115–128 (2001). https://doi.org/10.1023/A:1013318508043
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DOI: https://doi.org/10.1023/A:1013318508043