resources:roadmaps:from_symmetry
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| ====== Physics from Symmetry ====== | ====== Physics from Symmetry ====== | ||
| - | <note tip>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 [[:roadmaps|here]]. </note> | ||
| - | The idea of this roadmap is, in some sense, to turn the [[roadmaps:traditional|traditional roadmap]] upside down. Instead of starting with only approximately correct theories (Classical mechanics, Classical electrodynamics) and then slowly moving toward the more correct ones (Quantum Mechanics, Quantum Field Theory), here we start with the best theories of nature that we have. | + | The idea of this roadmap is, in some sense, to turn the [[resources:roadmaps:traditional|traditional roadmap]] upside down. Instead of starting with only approximately correct theories (Classical mechanics, Classical electrodynamics) and then slowly moving toward the more correct ones (Quantum Mechanics, Quantum Field Theory), here we start with the best theories of nature that we have. |
| - | The modern theories can be derived straight-forwardly from the principles of special relativity and using symmetry arguments. The older classical theories can then be understood as approximations of the modern theories. | + | The modern theories can be derived straight-forwardly from the principles of special relativity and using [[basic_tools:symmetry|symmetry arguments]]. The older classical theories can then be understood as approximations of the modern theories. |
| - | + | ||
| - | One advantage of this approach is that less time is spent on only approximately correct theories, and more time on the best theories of nature that we have. In addition, this approach show the connection between the various theories clearer than the traditional approach. | + | |
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| - | + | ||
| - | | + | |
| + | One advantage of this approach is that less time is spent on only approximately correct theories, and more time on the best theories of nature that we have. In addition, this approach shows the connection between the various theories clearer than the traditional approach. | ||
| + | Here is the general outline: | ||
| <diagram> | <diagram> | ||
| - | | Special Relativity|~@2| inertial frames of reference, Minkowski metric, Lorentz transformations| | + | | AA|~@2| inertial frames of reference, Minkowski metric, Lorentz transformations|AA=[[theories:classical_theories:special_relativity]] |
| | |!@4| | | | | | | | |!@4| | | | | | | ||
| - | | Group Theory|~@2| Lie algebras, representation theory, $SO(3)$, $SU(2)$, Lorentz group, spinors | | + | | BB|~@2| Lie algebras, representation theory, SO(3), SU(2), Lorentz group, spinors |BB=[[advanced_tools:group_theory]] |
| | |!@4| | | | | | | | |!@4| | | | | | | ||
| - | | Lagrangian Framework|~@2| Variational Calculus, Noether's Theorem| | + | |XYX|~@2| Variational Calculus, Noether's Theorem|XYX=[[frameworks:lagrangian_formalism|Lagrangian Framework]] |
| | |!@4| | | | | | | | |!@4| | | | | | | ||
| - | | Fundamental Equations|~@2| Klein-Gordon equation, Dirac equation, Maxwell equations, Proca equations, Canonical commutation relations | | + | | FEQ|~@2| Klein-Gordon equation, Dirac equation, Maxwell equations, Proca equations, Canonical commutation relations |FEQ=[[:equations]] |
| | |!@4| | | | | | | | |!@4| | | | | | | ||
| - | | Gauge Theory|~@2| internal symmetries, minimal coupling, Lagrangians for interacting particles/fields | | + | | ZZZ|~@2| internal symmetries, minimal coupling, Lagrangians for interacting particles/fields |ZZZ=[[theories:yang-mills_theory]] |
| | |!@4| | | | | | | | |!@4| | | | | | | ||
| - | | Quantum Mechanics|~@2| Schrödinger equation, particle in a box, double-slit experiment, Dirac notation | | + | | ZAZ|~@2| Schrödinger equation, particle in a box, double-slit experiment, Dirac notation |ZAZ=[[theories:quantum_theory:quantum_mechanics|]] |
| | |!@4| | | | | | | | |!@4| | | | | | | ||
| - | | Quantum Field Theory|~@2| Fourier expansion, canonical quantization, Pauli principle, scattering theory | | + | | QFT|~@2| Fourier expansion, canonical quantization, Pauli principle, scattering theory |QFT=[[theories:quantum_theory:quantum_field_theory]] |
| | |!@4| | | | | | | | |!@4| | | | | | | ||
| - | | Classical Electrodynamics|~@2| Coulomb potential, Lorentz force law | | + | | CE|~@2| Coulomb potential, Lorentz force law |CE=[[theories:classical_theories:electrodynamics]] |
| | |!@4| | | | | | | | |!@4| | | | | | | ||
| - | | Classical Mechanics|~@2| Newton's second law | | + | | CME|~@2| Newton's second law |CME=[[theories:classical_theories:classical_mechanics]] |
| </diagram> | </diagram> | ||
| + | |||
| The journey begins with the fundamental postulates of special relativity. These can be used to derive the Minkwoski metric, which is crucial for everything that follows. | The journey begins with the fundamental postulates of special relativity. These can be used to derive the Minkwoski metric, which is crucial for everything that follows. | ||
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| There is a book called "[[http://physicsfromsymmetry.com/|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. | There is a book called "[[http://physicsfromsymmetry.com/|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. | ||
| + | |||
| + | Here are some concrete further reading recommendations | ||
| + | |||
| + | <diagram> | ||
| + | | AA|~@2| a basic understanding of the fundamental idea is sufficient. A recommended book is Special Relativity by French|AA=[[theories:classical_theories:special_relativity]] | ||
| + | | |!@4| | | | | | | ||
| + | | BB|~@2| a deep understanding of group theory is essential. Two books that provide sufficient background are: "An Introduction to Tensors and Group Theory for Physicists" by Jeevanjee and "Naive Lie Theory" by Stillwell|BB=[[advanced_tools:group_theory]] | ||
| + | | |!@4| | | | | | | ||
| + | | XYX|-@2| the basic ideas as outlined here in the travel guide are enough. To get a deeper understanding "The Lazy Universe" by Jennifer Coopersmith is highly recommended.|XYX=[[frameworks:lagrangian_formalism|Lagrangian Framework]] | ||
| + | | |!@4| | | | | | | ||
| + | | EQTS|~@2| Klein-Gordon equation, Dirac equation, Maxwell equations, Proca equations, Canonical commutation relations |EQTS=[[:equations|]] | ||
| + | | |!@4| | | | | | | ||
| + | | ZZZ|~@2| again, the basic idea as described here in the travel guide is enough. |ZZZ=[[theories:yang-mills_theory|]] | ||
| + | | |!@4| | | | | | | ||
| + | | ZAZ|~@2| quantum mechanics should be understood on the level of the Feynman Lectures on Physics Vol. 3 and "Quantum Mechanics" by Griffith |ZAZ=[[theories:quantum_theory:quantum_mechanics|]] | ||
| + | | |!@4| | | | | | | ||
| + | | QFT|~@2| to understand quantum field theory, "Student Friendly Quantum Field Theory" by Klauber is perfect. |QFT=[[theories:quantum_theory:quantum_field_theory]] | ||
| + | | |!@4| | | | | | | ||
| + | | CE|~@2| electrodynamics should be understood on the level of the Feynman Lectures on Physics Vol. 2 and "Electrodynamics" by Griffith |CE=[[theories:classical_theories:electrodynamics]] | ||
| + | | |!@4| | | | | | | ||
| + | | CME|~@2| a thorough understanding of classical mechanics is provided, for example, by "Introduction to Classical Mechanics" by Morin |CME=[[theories:classical_theories:classical_mechanics]] | ||
| + | </diagram> | ||
| + | |||
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