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Wintersemester 2021/22

Geometric Quantization

Status of the Lecture Notes

The changes and developments of the versions of the Lecture Notes are reported in the following:
  • uploaded 06.06.23: Version 14.0 with 357 pages. Attention! There ist a discrepancy in Half-Density Quantization in the notes, see footnote 67 on page 195, I do not know to solve it! Changes in comparison to version 13.0:
    • Chapter 11 on Half-Density Quantization is split into 3 new chapters: 11,12,13!
    • Chapter 12 is moved to Chapter 15 an adapted, it is not complete yet.
    • Several small amendments in Chapter 1-10,
  • uploaded 19.09.22: Version 13.0 with 333 pages. Changes in comparison to version 12.2:
    • Several Amendments in Chapter 1-10, in particular ch. 4 Connections and ch. 7 Prequantization
    • Chapter 11: Substantially enlarged and partly rewritten
    • Chapter 12 & 13 newly organized. Not completed yet.
  • uploaded 19.06.22: Version 12.2 with 288 pages. Changes in comparison to version 12.1:
    • Amendments in Chapter 11 "Half-Density Quantization" concerning Bohr-Sommerfeld condition
    • Corrections in some chapters
  • uploaded 29.05.22: Version 12.1 with 284 pages. Changes in comparison to version 11.7:
    • First section of Chapter 12 "Half-form Quantization"
    • Further Amendments in Chapter 11 "Half-Density Quantization"
    • Amendments to examples in Chapter 1: The case M=T*Q
    • Discussing T*Q in later chapters (integrality, ... )
    • Additional longer section on self-adjoint operators in Appendix "Quantum Mechanics"
    • Corrections in some chapters
  • uploaded 28.04.22: Version 11.7 with 262 pages. Changes in comparison to version 11.5:
    • Additional section "Half-density pairing" in Chapter 11
    • Further Amendments and reorganization in Chapter 11 "Half-Density Quantization"
    • Corrections in some chapters
  • uploaded 23.04.22: Version 11.5 with 256 pages. Changes in comparison to version 11.0:
    • Additional section "Polarized Sections" in Chapter 10
    • Preliminary Completion Chapter 11 "Half-Density Quantization"
    • Corrections in various chapters
  • uploaded 17.03.22: Version 11.0 with 235 pages. Changes in comparison to version 10.9:
    • Amendments to the Appendix on Lie theory
    • Begin Chapter 11 "Half-Density Quantization"
    • Corrections in various chapters
  • uploaded 07.03.22: Version 10.9 with 230 pages. Changes in comparison to version 10.7:
    • Completion and reorganization of the Appendix on Lie theory
    • Amendments to Chapter Chapter 10 "Representation Space"
    • Amendments to Chapter 9 "Polarization"
    • Small corrections in various chapters
  • uploaded 13.02.22: Version 10.7 with 223 pages. Changes in comparison to version 10.4:
    • Complements in Chapter Chapter 10 "Representation Space"
    • Amandments to Chapter 9 "Polarization"
    • Chapter 11 "Metaplectic Correction" deleted (will be newly organized)
  • uploaded 03.02.22: Version 10.4 with 218 pages. Changes in comparison to version 10.3:
    • Small corrections in Chapter Chapter 10 "Representation Space"
    • Amandments to Chapter 9 "Polarization"
  • uploaded 02.02.22: Version 10.3 with 216 pages. Changes in comparison to version 10.0:
    • Shift of old sketch "Metaplectic Correction" to Chapter 11
    • Sketch of new Chapter 10 "Representation Space"
    • Reorganiation of Chapter 9 "Polarization"
    • Amendments in Chapter 8 "Integrality"
    • Corrections in several places
  • uploaded 26.01.22: Version 10.0 with 212 pages. Changes in comparison to version 9.2:
    • Sketch of new Chapter 10 "Metaplectic Correction"
    • Improvements in Chapter 9 "Polarization"
    • Improvements in Chapter 8 "Integrality"
    • Corrections in Lie Theory and elsewhere
    • List of sign conventions
  • uploaded 21.01.22: Version 9.2 with 202 pages. Changes in comparison to version 9.1:
    • Improvements in Chapter 8 "Integrality"
  • uploaded 20.01.22: Version 9.1 with 201 pages. Changes in comparison to version 9.0:
    • Small improvement in Chapter 8 "Integrality"
  • uploaded 20.01.22: Version 9.0 with 200 pages. Changes in comparison to version 8.0:
    • Small complements to Chapter 7 "Prequantization"
    • Greater complements to Chapter 8 "Integrality"
    • New Chapter 9 "Polarisation"
    • Complements to Appendix on Lie Theory
    • Several smaller corrections
  • uploaded 12.01.22: Version 8.0 with 174 pages. Changes in comparison to version 7.8:
    • Complements to Chapter 7 "Prequantization"
    • A new Chapter 8 "Integrality"
    • A new Section "CCR" in Chapter F "Quantum Mechanics" in the Appendix
    • Elementary complements to the postulates in the first section of Chapter F
    • Complements to Chapter C: Heisenberg Group
    • Several smaller corrections
  • uploaded 30.12.21: Version 7.8 with 161 pages. Changes in comparison to version 7.0:
    • A new Chapter "Cohomology" in the Appendix
    • A new Section "Quotients" in Chapter A "Manifolds": Elementary complements to topological and differentiable quotients
    • Begin of a new Chapter in the Appandix on Quantum Mechanical Systems
    • Several small corrections
  • uploaded 16.12.21: Version 7.0 with 137 pages. Changes in comparison to version 6.8:
    • Chapter 7 on "Prequantization"
    • complements to Chapter B "Complex Analysis"
    • complements Chapter 6 "Hermitian and Holomorphic Line Bundles"
    • corrections Chapter A and 2,4,5
  • uploaded 14.12.21: Version 6.8 with 130 pages. Changes in comparison to version 6.5:
    • complements Chapter 1, in particular with respect to Liouville form
    • complements Chapter 2, in particular discussion about constant c and calculations concernig prequantization for the simple case
    • expansion of Chapter B2 "Complex Analysis", in particular, illustration for the Kugelsatz and description of (r,s)-forms
    • corrections Chapter 6 "Hermitian and Holomorphic Line Bundles" and in 4,5
  • uploaded 08.12.21: Version 6.5 with 125 pages. Changes in comparison to version 6.0:
    • new Chapter 6 "Hermitian and Holomorphic Line Bundles"
    • expansion of Chapter B "Complex Analysis", in particular, new sections
    • small corrections in Chapter 3, 4, 5 and in Chapter A
    • begin new Chapter 7
  • uploaded 02.12.2021: Version 6.0 wit 112 pages. Changes in comparison to version 5.81:
    • small corrections in Chapter 4 "Connections"
    • corrections in Chapter 5 "Parallel Transport and Curvature"
    • new sections "Curvature", "Integrality Conditions"
    • small changes in Chapter B "Complex Analysis"
  • uploaded 29.11.2021: Version 5.81 with 106 pages.