Lectures on the Geometric Anatomy of Theoretical Physics

2021-02-24T10:17:13Z

Bollu: Textbook recommendations

{{Stub}}
by Dr. Frederic P Schuller

[[File:Geometric-physics.png|right]]

== 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=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
# 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

Lectures on the Geometric Anatomy of Theoretical Physics

2021-02-23T23:33:36Z

Bollu: Update all links to lectures

{{Stub}}
by Dr. Frederic P Schuller

[[File:Geometric-physics.png|right]]

== 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=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]
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Lectures on the Geometric Anatomy of Theoretical Physics

Lectures on the Geometric Anatomy of Theoretical Physics