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resources:roadmaps:from_symmetry
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Table of Contents
Physics from Symmetry
This is a "general" roadmap, which means it's not very detailed. For more details on how to learn the various subjects, have a look at the more specific roadmaps, listed here.
| Special Relativity | inertial frames of reference, Minkowski metric, Lorentz transformations | |||||||||||||
| Group Theory | Lie algebras, representation theory, $SO(3)$, $SU(2)$, Lorentz group, spinors | |||||||||||||
| Lagrangian Framework | Variational Calculus, Noether's Theorem | |||||||||||||
| Fundamental Equations | Klein-Gordon equation, Dirac equation, Maxwell equations, Proca equations | |||||||||||||
| Quantum Mechanics | Schrödinger equation, particle in a box, Dirac notation | |||||||||||||
| Quantum Field Theory | Fourier expansion, canonical quantization, scattering theory | |||||||||||||
| Electrodynamics | Coulomb potential, Lorentz force law | |||||||||||||
| Classical Mechanics | Newton's second law | |||||||||||||
Mathematical Tools
Crucial puzzle pieces that are missing in the above roadmap are mathematical tools. These are best learned when they are actually needed. This means, whenever you are trying to understand some topic like, for example, quantum mechanics, and a mathematical concept that you don't know is used, simply learned it then.
Here is a (incomplete) list of mathematical tools that are crucial for the topics listed above:
- Vector calculus: basis vectors, change of coordinate systems, matrix multiplication, scalars, right-handed and left-handed coordinate systems
- Calculus: product rule, integration by parts, Taylor series expansion, series, index notion, Kronecker symbol, Levi-Civita symbol
- Linear Algebra: conjugation and transposition of matrices, matrix exponential function, determinants, eigenvalues and eigenvectors, diagonalization of matrices.
- Misc: Fourier transform, Delta distribution
Recommended Books
There is a book called "Physics from Symmetry", that tries to implement the roadmap outlined above. However, of course, additional books are needed to understand each topic mentioned here fully.
resources/roadmaps/from_symmetry.1512916378.txt.gz · Last modified: 2017/12/10 14:32 (external edit)
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