Electromagnetics

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

• Lagrangian formulation of electromagetism

 

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
  

 

 

related items

• Gauge theory
  
• QED
  

 

 

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