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Lectures on the Geometric Anatomy of Theoretical Physics: Difference between revisions
Lectures on the Geometric Anatomy of Theoretical Physics (edit)
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by Dr. Frederic P Schuller | by Dr. Frederic P Schuller | ||
[[File:Geometric-physics.png]] | [[File:Geometric-physics.png|right]] | ||
== Lectures == | == 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] | ||
# | # [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=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 == | == Lecture Notes == | ||
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* [https://www.reddit.com/r/math/comments/77zdq3/lecture_notes_for_frederic_schullers_lectures_on/ Lecture Notes via Reddit by Simon Rea] | * [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] | * [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}} | |||