Geometric quantization of the Hitchin system
2017 ◽
Vol 14
(04)
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pp. 1750064
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This paper is about geometric quantization of the Hitchin system. We quantize a Kahler form on the Hitchin moduli space (which is half the first Kahler form defined by Hitchin) by considering the Quillen bundle as the prequantum line bundle and modifying the Quillen metric using the Higgs field so that the curvature is proportional to the Kahler form. We show that this Kahler form is integral and the Quillen bundle descends as a prequantum line bundle on the moduli space. It is holomorphic and hence one can take holomorphic square integrable sections as the Hilbert space of quantization of the Hitchin moduli space.
2017 ◽
Vol 14
(10)
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pp. 1750144
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2018 ◽
Vol 167
(01)
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pp. 61-64
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1998 ◽
Vol 10
(05)
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pp. 705-721
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Keyword(s):
2008 ◽
Vol 19
(04)
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pp. 387-420
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Keyword(s):
2009 ◽
Vol 20
(08)
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pp. 1029-1055
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