"Electromagnetics"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
imported>Pythagoras0
 
(사용자 2명의 중간 판 9개는 보이지 않습니다)
1번째 줄: 1번째 줄:
−
==gauge invariance==
+
==basic history==
 +
* Leyden jar : capacitor
 +
* Volta vs Galvani
 +
* Humphrey Davy
 +
* Oesrsted
 +
* Faraday
 +
* Maxwell
 +
* Lodge
 +
* Marconi
 +
* Tesla : alternating current
  
−
*  the electromagnetic potential is a connection on a U(1)-bundle on spacetime whose curvature is the electromagnetic field<br>
 
−
*  the electromagnetism is a gauge field theory with structure group U(1)<br>
 
  
−
 
 
  
−
 
+
==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==
 
==Lorentz force==
−
 
 
* almost all forces in mechanics are conservative forces, those that are functions only of positions, and certainly not functions of velocities
 
* 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
 
* Lorentz force is a rare example of velocity dependent force
  
−
 
+
  
−
 
+
  
 
==polarization of light==
 
==polarization of light==
−
 
+
*  has two possibilites
−
*  has two possibilites<br>
 
 
** what does this mean?
 
** what does this mean?
  
−
 
 
  
−
 
 
−
 
−
 
 
  
 
==Lagrangian formulation==
 
==Lagrangian formulation==
 +
* [[Lagrangian formulation of electromagetism]]
  
−
* Lagrangian for a charged particle in an electromagnetic field <math>L=T-V</math>
+
   
−
:<math>L(q,\dot{q})=m||\dot{q}||-e\phi+eA_{i}\dot{q}^{i}</math><br>
 
−
*  action
 
−
:<math>S=-\frac{1}{4}\int F^{\alpha\beta}F_{\alpha\beta}\,d^{4}x</math><br>
 
−
*  Euler-Lagrange equations
 
−
:<math>p_{i}=\frac{\partial{L}}{\partial{\dot{q}^{i}}}=m\frac{\dot{q}_{i}}{||\dot{q}_{i}||}+eA_{i}=mv_{i}+eA_{i}</math>
 
−
$$
 
−
F_{i}=\frac{\partial{L}}{\partial{q^{i}}}=\frac{\partial}{\partial{{q}^{i}}}(eA_{j}\dot{q}^{j})=e\frac{\partial{A_{j}}}{\partial{q}^{i}}\dot{q}^{j}
 
−
$$
 
−
*  equation of motion<br><math>\dot{p}=F</math> Therefore we get
 
−
:<math>m\frac{dv_{i}}{dt}=eF_{ij}\dot{q}^{j}</math>. This is what we call the Lorentz force law.<br>
 
−
* force on a particle is same as <math>e\mathbf{E}+e\mathbf{v}\times \mathbf{B}</math>
 
−
 
 
−
* http://dexterstory.tistory.com/888<br>
 
−
* [[path integral formulation of quantum mechanics|path integral]]<br>
 
−
 
 
−
 
 
−
 
 
−
 
 
  
 
==Hamiltonian formulation==
 
==Hamiltonian formulation==
 +
*  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
 +
**  similar to covariant derivative
  
−
*  total energy of a charge particle in an electromagnetic field<br><math>E=\frac{1}{2m}(p_j-eA_{j})(p_j-eA_j)+q\phi</math><br>
 
−
*  replace the momentum with the canonical momentum<br>
 
−
**  similar to covariant derivative<br>
 
  
−
 
 
−
 
−
 
 
  
 
==force on a particle==
 
==force on a particle==
 +
* 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]<br>
+
* [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<br>
+
*  Feynman's proof of Maxwell equations and Yang's unification of electromagnetic and gravitational Aharonov–Bohm effects
−
 
 
−
 
 
  
−
 
 
  
 
==related items==
 
==related items==
  
−
* [[Gauge theory]]<br>
+
* [[Gauge theory]]
−
* [[QED]]<br>
+
* [[QED]]
−
 
 
−
 
 
  
−
 
 
  
 
==encyclopedia==
 
==encyclopedia==
100번째 줄: 72번째 줄:
 
* http://en.wikipedia.org/wiki/Four-current
 
* http://en.wikipedia.org/wiki/Four-current
  
−
 
+
  
−
 
+
  
 
==books==
 
==books==
 +
* ELECTROMAGNETIC THEORY AND COMPUTATION
 +
* [[The Early History of Radio from Faraday to Marconi]]
  
−
ELECTROMAGNETIC THEORY AND COMPUTATION
+
 
[[분류:math and physics]]
 
[[분류:math and physics]]
 +
[[분류:gauge theory]]
 +
[[분류:migrate]]
 +
 +
==메타데이터==
 +
===위키데이터===
 +
* ID :  [https://www.wikidata.org/wiki/Q377930 Q377930]
 +
===Spacy 패턴 목록===
 +
* [{'LOWER': 'classical'}, {'LEMMA': 'electromagnetism'}]
 +
* [{'LEMMA': 'electrodynamic'}]

2021년 2월 17일 (수) 03:16 기준 최신판

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


related items


encyclopedia



books

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'classical'}, {'LEMMA': 'electromagnetism'}]
  • [{'LEMMA': 'electrodynamic'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Electromagnetics&oldid=51946"