resources:roadmaps:from_symmetry
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resources:roadmaps:from_symmetry [2017/12/10 17:04] jakobadmin |
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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 shows the connection between the various theories clearer than the traditional approach. | 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. | ||
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| | AA|~@2| inertial frames of reference, Minkowski metric, Lorentz transformations|AA=[[theories:classical_theories:special_relativity]] | | AA|~@2| inertial frames of reference, Minkowski metric, Lorentz transformations|AA=[[theories:classical_theories:special_relativity]] | ||
| | |!@4| | | | | | | | |!@4| | | | | | | ||
| - | | BB|~@2| CC, representation theory, SO(3), SU(2), Lorentz group, spinors |BB=[[advanced_tools:group_theory]]|CC=[[advanced_tools:lie_algebras]]|DD=[[advanced_tools: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> | ||
| Line 68: | Line 67: | ||
| Here are some concrete further reading recommendations | Here are some concrete further reading recommendations | ||
| - | |||
| - | |||
| <diagram> | <diagram> | ||
| - | | [[theories:classical_theories:special_relativity|Special Relativity]]|~@2| a basic understanding of the fundamental idea is sufficient. A recommended book is Special Relativity by French| | + | | 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| | | | | | | | |!@4| | | | | | | ||
| - | | Group Theory|~@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|~@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| | | | | | | | |!@4| | | | | | | ||
| - | | Lagrangian Framework|~@2| the basic ideas as outlined [[frameworks:lagrangian_formalism|here]] are enough. To get a deeper understanding "The Lazy Universe" by Jennifer Coopersmith is highly recommended.| | + | | 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| | | | | | | | |!@4| | | | | | | ||
| - | | understanding the derivation of the [[:equations|Fundamental Equations]]|~@2| [[equations:klein-gordon_equation|Klein-Gordon equation]], [[equations:dirac_equation|Dirac equation]], [[equations:maxwell_equations|Maxwell equations]], Proca equations from the from the corresponding Lagrangian is essential. These are shown, for example, in "Physics from Symmetry" by Schwichtenberg.| | + | | EQTS|~@2| Klein-Gordon equation, Dirac equation, Maxwell equations, Proca equations, Canonical commutation relations |EQTS=[[:equations|]] |
| | |!@4| | | | | | | | |!@4| | | | | | | ||
| - | | [[theories:yang-mills_theory|Gauge Theory]]|~@2| again, the basic idea as described here in the travel guide is enough. | | + | | ZZZ|~@2| again, the basic idea as described here in the travel guide is enough. |ZZZ=[[theories:yang-mills_theory|]] |
| | |!@4| | | | | | | | |!@4| | | | | | | ||
| - | | [[theories:quantum_theory:quantum_mechanics|Quantum Mechanics]]|~@2| quantum mechanics should be understood on the level of the Feynman Lectures on Physics Vol. 3 and "Quantum Mechanics" by Griffith | | + | | 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| | | | | | | | |!@4| | | | | | | ||
| - | | [[theories:quantum_theory:quantum_field_theory|Quantum Field Theory]]|~@2| to understand quantum field theory, "Student Friendly Quantum Field Theory" by Klauber is perfect. | | + | | QFT|~@2| to understand quantum field theory, "Student Friendly Quantum Field Theory" by Klauber is perfect. |QFT=[[theories:quantum_theory:quantum_field_theory]] |
| | |!@4| | | | | | | | |!@4| | | | | | | ||
| - | | [[theories:classical_theories:electrodynamics|Classical Electrodynamics]]|~@2| electrodynamics should be understood on the level of the Feynman Lectures on Physics Vol. 2 and "Electrodynamics" by Griffith | | + | | 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| | | | | | | | |!@4| | | | | | | ||
| - | | [[theories:classical_theories:classical_mechanics|Classical Mechanics]]|~@2| a thorough understanding of classical mechanics is provided, for example, by "Introduction to Classical Mechanics" by Morin | | + | | 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> | </diagram> | ||
| + | |||
resources/roadmaps/from_symmetry.1512921888.txt.gz · Last modified: 2017/12/10 16:04 (external edit)
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