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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeOct 6th 2011

gave prequantum line bundle a little entry of its own

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeOct 6th 2011

People also say “quantization line bundle”.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeOct 6th 2011

Yes, many more people say “quantum line bundle”. But some say “prequantum line bundle”. On the other hand, everybody says that constructing these beasts is “prequantization”, so the latter term seems to make more sense.

• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeOct 6th 2011

I do not know of quantum line bundle, I heard more often quantization line bundle (what makes more sense, the bundle is not quantum but it is used for quantization).

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeOct 6th 2011

That’s true.

• CommentRowNumber6.
• CommentAuthorzskoda
• CommentTimeOct 7th 2011

Just to remind (if somebody did not notice) of the recent related entry orbit method, which was the principal source (along with rather complementary Borel-Weil-Bott theorem), historically, of the geometric quantization.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJul 16th 2015
• (edited Jul 16th 2015)

• Jack Morava, Cobordism of symplectic manifolds and asymptotic expansions, talk at the conference in honor of S.P. Novikov’s 60th birthday (arXiv:9908070)

which discusses prequantized manifolds in the context of cobordism rings and Thom spectra. (Thanks to Jack Morava for pointing this reference out to me.)

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