I have tried to expand the Idea-section at *orbit method* a little.

started *Guillemin-Sternberg geometric quantization conjecture*

So far just the brief Idea and a few commented references.

]]>I want to collect, for expositional purpose, in one place all the ingredients that go into the story of *geometric quantization of the 2-sphere*, a simple and archetypical example of geometric quantization.

So far I have included everything (I think) pertaining to the prequantum line bundles, the polarization and the spaces of quantum states. Next I’ll add discussion of the angular momentum quantum operators.

]]>I am back to working on *geometry of physics*. I’ll be out-sourcing new paragraphs there to their own $n$Lab entries as much as possible (because the length of the page makes saving and hence previewing it take many minutes, so I need to work in smaller sub-entries and then copy-and-paste).

In this context I now started an entry *prequantum field theory*. To be further expanded.

This comes with a table of related concepts *extended prequantum field theory - table*:

**extended prequantum field theory**

$0 \leq k \leq n$ | transgression to dimension $k$ |
---|---|

$0$ | extended Lagrangian, universal characteristic map |

$k$ | (off-shell) prequantum (n-k)-bundle |

$n-1$ | (off-shell) prequantum circle bundle |

$n$ | action functional = prequantum 0-bundle |

created some bare minimum at *symplectic spinors* and *metaplectic quantization*

wrote the first part of a discussion of *prequantized Lagrangian correspondences*, showing how traditional Hamiltonian and Lagrangian mechanics are naturally absorbed into the context of “local prequantum field theory” and “motivic quantization”.

Simple as it is, but does anyone know if the proposition in the section *The classical action functional prequantizes Hamiltonian correspondences* has been made explicit in the literature before? I can’t find it, but it should have been discussed before. If anyone has a citation, please let me know. Of course all the ingredients of the little proof are simple classical steps, but I am wondering if this has been observed as a statement, simple as it may be, on the prequantum lift of the more famous Lagrangian correspondences.

started a minimum at *p-convex polarization*

as mentioned in another thread, I have expanded the Idea-section at *polarization* in order to highlight the relation to *canonical momenta* (which I also edited accordingly).

Just in case you see me editing in the *Recently Revised* list and are wondering:

I have created and have started to fill some content into *semiclassical state*. But I am not done yet and the entry is not in good shape yet. So don’t look at yet it unless in a mood for fiddling and editing.

I have started something at Bohr-Sommerfeld leaf, but need to continue later when I have more time and energy

]]>Since I found myself repeatedly referring to it from other $n$Lab entries, I finally put some content into the entry *extended Lagrangian*.

brief note on *geometric quantization of non-integral 2-forms*

I have splitt off Hamiltonian vector field from symplectic manifold in order to also record the $n$-plectic generalization.

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