"Electromagnetics"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 14번째 줄: | 14번째 줄: | ||
==gauge invariance== | ==gauge invariance== | ||
| − | * the electromagnetic potential is a connection on a U(1)-bundle on spacetime whose curvature is the electromagnetic field | + | * the electromagnetic potential is a connection on a U(1)-bundle on spacetime whose curvature is the electromagnetic field |
| − | * the electromagnetism is a gauge field | + | * the electromagnetism is a gauge field theory with structure group U(1) |
| − | + | ||
| − | + | ||
==Lorentz force== | ==Lorentz force== | ||
| 26번째 줄: | 26번째 줄: | ||
* Lorentz force is a rare example of velocity dependent force | * Lorentz force is a rare example of velocity dependent force | ||
| − | + | ||
| − | + | ||
==polarization of light== | ==polarization of light== | ||
| − | * has two possibilites | + | * has two possibilites |
** what does this mean? | ** what does this mean? | ||
| − | + | ||
| − | + | ||
| − | + | ||
==Lagrangian formulation== | ==Lagrangian formulation== | ||
* [[Lagrangian formulation of electromagetism]] | * [[Lagrangian formulation of electromagetism]] | ||
| − | + | ||
==Hamiltonian formulation== | ==Hamiltonian formulation== | ||
| − | * total energy of a charge particle in an electromagnetic field | + | * total energy of a charge particle in an electromagnetic field<math>E=\frac{1}{2m}(p_j-eA_{j})(p_j-eA_j)+q\phi</math> |
| − | * replace the momentum with the canonical momentum | + | * replace the momentum with the canonical momentum |
| − | ** similar to covariant derivative | + | ** similar to covariant derivative |
| − | + | ||
| − | + | ||
==force on a particle== | ==force on a particle== | ||
| 60번째 줄: | 60번째 줄: | ||
* force on a particle is same as <math>e\mathbf{E}+e\mathbf{v}\times \mathbf{B}</math> | * force on a particle is same as <math>e\mathbf{E}+e\mathbf{v}\times \mathbf{B}</math> | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
==메모== | ==메모== | ||
| − | * [http://www.math.toronto.edu/%7Ecolliand/426_03/Papers03/C_Quigley.pdf http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Quigley.pdf] | + | * [http://www.math.toronto.edu/%7Ecolliand/426_03/Papers03/C_Quigley.pdf http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Quigley.pdf] |
| − | * Feynman's proof of Maxwell equations and Yang's unification of electromagnetic and gravitational Aharonov–Bohm effects | + | * Feynman's proof of Maxwell equations and Yang's unification of electromagnetic and gravitational Aharonov–Bohm effects |
| − | + | ||
| − | + | ||
==related items== | ==related items== | ||
| − | * [[Gauge theory]] | + | * [[Gauge theory]] |
| − | * [[QED]] | + | * [[QED]] |
| − | |||
| − | |||
| − | |||
==encyclopedia== | ==encyclopedia== | ||
| 96번째 줄: | 93번째 줄: | ||
* http://en.wikipedia.org/wiki/Four-current | * http://en.wikipedia.org/wiki/Four-current | ||
| − | + | ||
| − | + | ||
==books== | ==books== | ||
* ELECTROMAGNETIC THEORY AND COMPUTATION | * ELECTROMAGNETIC THEORY AND COMPUTATION | ||
| + | * [[The Early History of Radio from Faraday to Marconi]] | ||
| + | |||
[[분류:math and physics]] | [[분류:math and physics]] | ||
[[분류:gauge theory]] | [[분류:gauge theory]] | ||
2013년 9월 22일 (일) 15:31 판
basic history
- Leyden jar : capacitor
- Volta vs Galvani
- Humphrey Davy
- Oesrsted
- Faraday
- Maxwell
- Lodge
- Marconi
- Tesla : alternating current
gauge invariance
- the electromagnetic potential is a connection on a U(1)-bundle on spacetime whose curvature is the electromagnetic field
- the electromagnetism is a gauge field theory with structure group U(1)
Lorentz force
- almost all forces in mechanics are conservative forces, those that are functions only of positions, and certainly not functions of velocities
- Lorentz force is a rare example of velocity dependent force
polarization of light
- has two possibilites
- what does this mean?
Lagrangian formulation
Hamiltonian formulation
- total energy of a charge particle in an electromagnetic field\(E=\frac{1}{2m}(p_j-eA_{j})(p_j-eA_j)+q\phi\)
- replace the momentum with the canonical momentum
- similar to covariant derivative
force on a particle
- force on a particle is same as \(e\mathbf{E}+e\mathbf{v}\times \mathbf{B}\)
메모
- http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Quigley.pdf
- Feynman's proof of Maxwell equations and Yang's unification of electromagnetic and gravitational Aharonov–Bohm effects
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Classical_electromagnetism
- http://en.wikipedia.org/wiki/Maxwell's_equations
- http://en.wikipedia.org/wiki/Maxwell's_equations#Differential_geometric_formulations
- http://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism
- http://en.wikipedia.org/wiki/electrical_current
- http://en.wikipedia.org/wiki/Four-current
books
- ELECTROMAGNETIC THEORY AND COMPUTATION
- The Early History of Radio from Faraday to Marconi