An approximation to an efficient fundamental physics curriculum
keywords
outline
see the latex / pdf version of this on overleaf and posted to my website log
Introduction
Basic question
What is an approximation to a physics curriculum that is co-optimized between the goals of being both comprehensive (up to the fringe of existing experimental verification, but not necessarily quite rigorous enough to prepare for original research) and efficient?
Before reviewing t proposed curriculum it would be reasonable to consider the much broader and more comprehensive perspective from Gerard ’t Hooft: How to become a GOOD Theoretical Physicist
Global perspective
I think it is helpful to be aware of the following perspectives before getting started
A quote regarding the relationship between the local and global structure of theoretical physics “All of physics has two aspects: a local or even infinitesimal aspect, and a global aspect. Much of the standard lore deals just with the local and infinitesimal aspects -* the __perturbative__ aspects and [[file:fiber_bundle.org]fiber bundles play little role there. But they are the all-important structure that governs the global -* the __non-perturbative__ -* aspect. Bundles are the __global__ structure of physical fields and they are irrelevant only for the crude local and perturbative description of reality.” [Note: Of course…the latter should not be viewed as a criticism as those are the components that support concrete calculations that make direct contact with the analysis of experiments] –[Urs Schreiber response to physics.stackexchange question: Intuitively, why are bundles so important in Physics?]] A paragraph written by Edward Witten p. 280 in the 1986 Proceedings of the International Congress of Mathematicians and on p. 20 in Physics and geometry by Edward Witten in 1986 (see below) taken with update from Eric Weinstein’s, The Portal ‘Graph, Wall, Tome project’ If one wants to summarize our knowledge of physics in the briefest possible terms, there are really three fundamental observations
- Space-time is a pseudo-Riemannian manifold, \[M\], endowed with a metric tensor and governed by geometrical laws
- Over \[M\] is a principal \[G\]-bundle, \[P_G\], with a non-Abelian structure group \[G\]
- Fermions are sections of \[\hat{S}_+ \otimes V_R \oplus \hat{S}_* \otimes V_{\tilde{R}}\]. \[R\] and \[\tilde{R}\] are not isomorphic, but should be complex linear representations of \[G\]
- ? Higgs
All of this must be supplemented with the understanding that the geometrical laws obeyed by the metric tensor, the gauge fields, and the fermions are to be interpreted in quantum mechanical terms.
Resources
Written texts (not necessarily in this order)
Overviews
General relativity
Quantum field theory
Statistical physics
Symmetry
Global structure
- [[file:Physics_and_geometry_by_Edward_Witten_in_1986.org]Physics and geometry by Edward Witten in 1986) ([link]]
- [[file:Geometry_of_physics_by_Urs_Schreiber.org]Geometry of physics by Urs Schreiber) ([link]]
Lectures
Overviews
General relativity
- What is a tensor? by XylyXylyX 39 videos
- What is a Manifold? by XylyXylyX 18 videos
- What is General Relativity? by XylyXylyX 66 videos
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[[file:A_thorough_introduction_to_the_theory_of_general_relativity_by_Frederic_Schuller_in_2015.org]A thorough introduction to the theory of general relativity by Frederic Schuller in 2015) ([playlist]]
Quantum field theory
- Lie Groups and Lie Algebras by XylyXylyX 41 videos
- Quantum field theory by Tobias Osborne 18 videos
Statistical physics
-
Large deviation theory in statistical physics at ICTP
- Especially the two lectures (part 1 ; part 2 by Hugo Touchette
Global structure
- [[file:Lectures_on_Geometrical_Anatomy_of_Theoretical_Physics_by_Frederic_Schuller_in_2015.org]Lectures on Geometrical Anatomy of Theoretical Physics by Frederic Schuller in 2015) ([playlist]]