Geometric quantization and no-go theorems

• Autorzy: Viktor L. Ginzburg , Richard Montgomery
• Języki publikacji: EN

Abstrakty

EN

A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist. This is a consequence of a "no-go" theorem claiming that the entire Lie algebra of smooth functions on a compact symplectic manifold cannot be quantized, i.e., it has no essentially nontrivial finite-dimensional representations.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2000
• Tom: 51
• Numer: 1
• Strony: 69-77

Daty

wydano

2000

Twórcy

autor

Viktor L. Ginzburg

• Department of Mathematics, University of California at Santa Cruz, Santa Cruz, CA 95064, U.S.A.

autor

Richard Montgomery

• Department of Mathematics, University of California at Santa Cruz, Santa Cruz, CA 95064, U.S.A.

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