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Questions on various methods and aspects of quantization

7 votes
2 answers
680 views

Deriving the Hilbert spaces for Chern-Simons TQFTs with complex gauge group

Is there a derivation of the state spaces for Chern-Simons TQFTs with gauge group $SL(n,\mathbb{C})$ that uses geometric quantization? … Equivalently, is there a geometric quantization of the $SL(n,\mathbb{C})$ character varieties of surfaces? Or at least for $n=2$? …
7 votes
1 answer
748 views

SL(2,C) Chern-Simons theory in genus 1

$L^2(T\times T)$ (which is what Witten claims to be the quantization of the moduli space). … However, if we take $\omega$ as the symplectic form, $\omega$ is non-zero in cohomology, and we will end up with a more complicated quantization. …
1 vote
1 answer
281 views

BKS pairing for distributional sections

I am trying to understand the Blattner-Kostant-Sternberg pairing as it applies to geometric quantization in real polarizations whose integral manifolds are, for simplicity, compact. … I have been trying to follow Sniatycki's account (Geometric Quantization and Quantum Mechanics, pp 73-75). …