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2000 | 51 | 1 | 69-77
Tytuł artykułu

Geometric quantization and no-go theorems

Treść / Zawartość
Warianty tytułu
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.
Słowa kluczowe
Rocznik
Tom
51
Numer
1
Strony
69-77
Opis fizyczny
Daty
wydano
2000
Twórcy
  • Department of Mathematics, University of California at Santa Cruz, Santa Cruz, CA 95064, U.S.A.
  • Department of Mathematics, University of California at Santa Cruz, Santa Cruz, CA 95064, U.S.A.
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv51z1p69bwm
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