From a working physicist's perspective, the conjecture of Guillemin-Sternberg (and its generalisations) seems to state in a highly technical manner that quantization commutes with gauge-fixing.

In how far has this conjecture been generalised and proven to be of practical use to QFT and string theory? Does it for instance back up the claim that gauge-fixing the string action in light-cone gauge and then quantising it is equivalent to quantising it first, and then removing unphysical states (covariant quantisation)?

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    $\begingroup$ ncatlab.org/nlab/show/… $\endgroup$ – Mitchell Porter Jul 7 '19 at 23:51
  • $\begingroup$ Thanks. I know this resource and the references within but it is too technical for me to understand. $\endgroup$ – Werner Einstein Jul 8 '19 at 7:09
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    $\begingroup$ Guillemin-Sternberg for string theory is conjectured to hold if the quantization is done "right", whatever that means, but it's unlikely that it's written down rigorously anywhere in all details. $\endgroup$ – Qmechanic Jul 8 '19 at 11:15
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    $\begingroup$ Just to elaborate on @Qmechanic's comment: you can do it "wrong" in which case light-cone gauge quantization and covariant quantization (of the string) disagree. "Wrong" includes the case of non-critical dimension. See Green-Schwarz-Witten $\endgroup$ – alexarvanitakis Jul 27 '19 at 20:48

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