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A case study of quantization on curved surfaces: the Mylar balloon. (English) Zbl 1057.53005
Slovák, Jan (ed.) et al., The proceedings of the 23th winter school “Geometry and physics”, Srní, Czech Republic, January 18–25, 2003. Palermo: Circolo Matemàtico di Palermo. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 72, 159-169 (2004).
The article describes the quantization of the Mylar balloon. The Mylar balloon is the unique surface of revolution whose principal curvatures satisfy \(\kappa_1=2\kappa_2\). It arises as the solution of a variational problem discussed in another paper by the author [see C. R. Acad. Bulg. Sci. 54, No. 9, 39–44 (2001; Zbl 0986.53002)]. To achieve the quantization of the free particle motion (geodesic flow) on the Mylar balloon the author uses a combination of the methods of constrained quantum mechanics and geometric quantization.
For the entire collection see [Zbl 1034.53002].
MSC:
53A05 Surfaces in Euclidean and related spaces
53D20 Momentum maps; symplectic reduction
53D25 Geodesic flows in symplectic geometry and contact geometry
53D50 Geometric quantization
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