Geometric Quantization

Status of the Lecture Notes

The changes and developments of the versions of the Lecture Notes are reported in the following:

• uploaded 23.03.25: Version 15.2 with 399 pages. Changes in comparison to version 15.1:
  • Corrections and amendments in Chapter 16 and 17.
  • New Chapter 18: Metaplectic Representation.
• uploaded 23.12.24: Version 15.1 with 391 pages. Changes in comparison to version 14.9:
  • Chapter 16 and 17: Correction, the description of the metalinear group in 14.9 and before is completely wrong.
• uploaded 30.10.24: Version 14.9 with 390 pages. Changes in comparison to version 14.5:
  • Chapter 16 and 17 completely new.
  • Amendments and corrections in Chapter 8, 9, 10, 12, 15
• uploaded 04.08.24: Version 14.5 with 377 pages. Not too much has been changed during the last two years. Changes in comparison to version 13.0:
  • Leitfaden at the end of contents
  • Chapter 10 has been devided into ch. 10 and 11
  • The former Chapter 11 on Half-Density Quantization is split into 3 new chapters: 12, 13, 14!
  • Chapter 12 on half-form quantization is now Chapter 15 in an adapted form, but this chapter is not complete yet.
  • The main work has been done in preparing several small amendments in the new Chapters 1-15 and the appendices, in particular in 9-14,
  • 15 & 16 (old 12 & 13) are still only sketches, not completed yet.
• 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.