Lectures on the Geometric Anatomy of Theoretical Physics: Difference between revisions

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by Dr. Frederic P Schuller
by Dr. Frederic P Schuller


[[File:Geometric-physics.png]]
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== Lectures ==
 
[https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic The entire playlist on YouTube.]


# [https://www.youtube.com/watch?v=V49i_LM8B0E Introduction/Logic of propositions and predicates]
# [https://www.youtube.com/watch?v=V49i_LM8B0E Introduction/Logic of propositions and predicates]
# Links to all of the lectures would be helpful...
# [https://www.youtube.com/watch?v=AAJB9l-HAZs&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=2 Axioms of set theory]
# [https://www.youtube.com/watch?v=6EIWRg-6ftQ&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=3 Classification of sets]
# [https://www.youtube.com/watch?v=1wyOoLUjUeI&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=4 Topological spaces: construction and purpose]
# [https://www.youtube.com/watch?v=hiD6Tz06k30&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=5 Topological spaces: some heavily used invariants]
# [https://www.youtube.com/watch?v=uGEV0Wk0eIk&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=6 Topological manifolds and manifold bundles]
# [https://www.youtube.com/watch?v=Fa6SRAwY80Y&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=7 Differentiable structures: definition and classification]
# [https://www.youtube.com/watch?v=4l-qzZOZt50&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=8 Tensor space theory I: Over a field]
# [https://www.youtube.com/watch?v=UPGoXBfm6Js&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=9 Differential structures: The pivotal concept of tangent vector spaces]
# [https://www.youtube.com/watch?v=XZcKSoI17r0&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=10 Construction of the tangent bundle]
# [https://www.youtube.com/watch?v=V0TPgeiyWCo&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=11 Tensor space theory II: Over a ring]
# [https://www.youtube.com/watch?v=QLnzIOGIvfo&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=12 Grassman algebra and De Rham cohomology]
# [https://www.youtube.com/watch?v=mJ8ZDdA10GY&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=13 Lie groups and their lie algebras]
# [https://www.youtube.com/watch?v=Vlbcd_lPNMA&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=14 Classification of lie algebras and their dynkin diagrams]
# [https://www.youtube.com/watch?v=H1D09cuFWlM&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=15 Lie group SL(2,C) and its algebra]
# [https://www.youtube.com/watch?v=G9uVcit_VwY&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=16 Dykin diagrams from Lie algebras and vice versa]
# [https://www.youtube.com/watch?v=h-d8TUg022A&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=17 Representation theory of lie groups and lie algebras]
# [https://www.youtube.com/watch?v=7qO5y6Es9Ns&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=18 Reconstruction of a Lie group from its algebra]
# [https://www.youtube.com/watch?v=vYAXjTGr_eM Principal fibre bundles]
# [https://www.youtube.com/watch?v=q2GYZz6q3QI&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=20 Associated fiber bundles]
# [https://www.youtube.com/watch?v=jFvyeufXyW0&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=21 Connections and Connection 1 forms]
# [https://www.youtube.com/watch?v=KhagmmNvOvQ&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=22 Local representations of a connection on the base manifold: Yang-Mills fields]
# [https://www.youtube.com/watch?v=jGHaZc2fuX8&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=23 Parallel transport]
# [https://www.youtube.com/watch?v=j36o4DLLK2k&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=24 Curvature and torsion on principal bundles]
# [https://www.youtube.com/watch?v=ClIVG7ilm_Q&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=25 Covariant derivatives]
# [https://www.youtube.com/watch?v=C93KzJ7-Es4&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=26 Application: Quantum mechanics on curved spaces]
# [https://www.youtube.com/watch?v=Way8FfcMpf0&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=27 Application: Spin structures]
# [https://www.youtube.com/watch?v=F3oGhXNhIDo&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=28 Application: Kinematical and dynamical symmetries]
 
== Lecture Notes ==
 
* [https://www.reddit.com/r/math/comments/77zdq3/lecture_notes_for_frederic_schullers_lectures_on/ Lecture Notes via Reddit by Simon Rea]
* [https://drive.google.com/file/d/1nchF1fRGSY3R3rP1QmjUg7fe28tAS428/view Lecture Notes PDF by Simon Rea]
 
== Textbooks ==
 
#  Shilov's Linear Algebra and Lang's Algebra as references
# Shlomo Sternberg's lectures on Differential Geometry to make sure you know your foundations and constructions
# Kobayashi Nomizu for more sophisticated basic theory
# Steenrod Topology of Fibre bundles
#  A basic course in Algebraic Topology, Hatcher or Spanier
# sheaf theoretic overview of modern(ish) Differential Geometry - Isu Vaisman's Cohomology and Differential forms
# good for exercises on G-bundle theory - Mathematical gauge theory by Hamilton
 
{{Stub}}

Latest revision as of 22:32, 14 May 2023

by Dr. Frederic P Schuller

Geometric-physics.png

Lectures[edit]

The entire playlist on YouTube.

  1. Introduction/Logic of propositions and predicates
  2. Axioms of set theory
  3. Classification of sets
  4. Topological spaces: construction and purpose
  5. Topological spaces: some heavily used invariants
  6. Topological manifolds and manifold bundles
  7. Differentiable structures: definition and classification
  8. Tensor space theory I: Over a field
  9. Differential structures: The pivotal concept of tangent vector spaces
  10. Construction of the tangent bundle
  11. Tensor space theory II: Over a ring
  12. Grassman algebra and De Rham cohomology
  13. Lie groups and their lie algebras
  14. Classification of lie algebras and their dynkin diagrams
  15. Lie group SL(2,C) and its algebra
  16. Dykin diagrams from Lie algebras and vice versa
  17. Representation theory of lie groups and lie algebras
  18. Reconstruction of a Lie group from its algebra
  19. Principal fibre bundles
  20. Associated fiber bundles
  21. Connections and Connection 1 forms
  22. Local representations of a connection on the base manifold: Yang-Mills fields
  23. Parallel transport
  24. Curvature and torsion on principal bundles
  25. Covariant derivatives
  26. Application: Quantum mechanics on curved spaces
  27. Application: Spin structures
  28. Application: Kinematical and dynamical symmetries

Lecture Notes[edit]

Textbooks[edit]

  1. Shilov's Linear Algebra and Lang's Algebra as references
  2. Shlomo Sternberg's lectures on Differential Geometry to make sure you know your foundations and constructions
  3. Kobayashi Nomizu for more sophisticated basic theory
  4. Steenrod Topology of Fibre bundles
  5. A basic course in Algebraic Topology, Hatcher or Spanier
  6. sheaf theoretic overview of modern(ish) Differential Geometry - Isu Vaisman's Cohomology and Differential forms
  7. good for exercises on G-bundle theory - Mathematical gauge theory by Hamilton
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