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BEREZIN–TOEPLITZ QUANTIZATION, HYPERKÄHLER MANIFOLDS, AND MULTISYMPLECTIC MANIFOLDS

Part of: Applications to physics - Differential geometry Symplectic geometry, contact geometry

Published online by Cambridge University Press:  10 June 2016

TATYANA BARRON  and
BARAN SERAJELAHI
TATYANA BARRON
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada e-mail: [email protected]
BARAN SERAJELAHI
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada e-mail: [email protected]
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Abstract

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We suggest a way to quantize, using Berezin–Toeplitz quantization, a compact hyperkähler manifold (equipped with a natural 3-plectic form), or a compact integral Kähler manifold of complex dimension n regarded as a (2n−1)-plectic manifold. We show that quantization has reasonable semiclassical properties.

MSC classification

Primary: 53D99: None of the above, but in this section
Secondary: 53Z05: Applications to physics
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 1 , January 2017 , pp. 167 - 187
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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