Electrodynamics and field theory 0800-PA-ELFIELD

1 Maxwell equations
1.1 Differential form
1.2 Integral form
1.3 Electrostatics and magnetostatics
1.4 Simple electric and magnetic configurations
1.5 Maxwells Equations in Matter

2 Conservation laws
2.1 Charge conservation
2.2 Energy conservation
2.3 Momentum conservation
2.4 Riemann-Silberstein vector

3 Electromagnetic waves in vacuum

4 Elements of special relativity theory
4.1 Minkowski space-time
4.2 Hyperbolic rotations and the geometry of light cones
4.3 Relativistic kinematics

5 Relativistic formulation of Maxwell equations
5.1 Electromagnetic potentials
5.2 Tensor calculus
5.3 Faraday field tensor
5.4 Equations for 4-potential
5.5 Transformation of electric and magnetic fields
5.6 Relativistic invariants
5.7 Electromagnetic field of uniformly moving charge
5.8 Lorentz force and dynamics of charges
5.9 Relativistic form of conservation laws
5.10 Relativistic definition of charge, energy and momentum

6. Solving Maxwell equations
6.1 How to solve the wave equation?
6.2 Solving for 4-potential
6.3 Covariant formulation
6.4 Lienard-Wiechert solution

7 Electromagnetic radiation
7.1 Radiation from the point charge
7.2 Hertz vector
7.3 Hertz dipole - dipole radiation

8 Lagrangian and Hamiltonian mechanics
8.1 Euler-Lagrange equations
8.2 Hamilton equations
8.3 Conservation laws

9 Lorentz group
9.1 Lorentz transformations in the 4D Minkowski space-time
9.2 Poincare group
9.3 How to realize on fields: Poincare algebra
9.4 Transformation properties of fields

10 Lagrangian field theory
10.1 Euler-Lagrange equations
10.2 Hamiltonian formulation
10.3 Scalar field
10.4 Complex scalar field
10.5 Lagrangian for the Maxwell field
10.6 Maxwell field + charged particle

11 Noether Theorem and conservation laws
11.1 General formulation
11.2 Translational invariance
11.3 Lorentz invariance
11.4 Energy-momentum tensor
11.5 Scalar field
11.5.1 Energy-momentum
11.5.2 Angular momentum

12 Gauge theory | scalar electrodynamics
12.1 Global gauge invariance
12.2 Local gauge invariance

13 Yang-Mills gauge theory
13.1 Global SU(2)-invariance
13.2 Local SU(2)-invariance
13.3 Gauge invariant Yang-Mills Lagrangian
13.4 Yang-Mills field equations