Lässig

research

group

Statistical Physics and Quantitative Biology

University of Cologne

Classical Theoretical Physics II: Advanced Mechanics and Electrodynamics

*Winter Semester 2009/2010*

- Lagrange mechanics
- Least action principle
- Lagrangian of a free particle, Galilei invariance
- Lagrangian mechanics in generalized coordinates
- Systems with boundary conditions and with constraints
- Symmetries and conservation laws

- Hamilton mechanics
- Legendre transformations
- Hamiltonian function and canonical equations of motion
- Symmetries and conservation laws in Hamiltonian mechanics
- Phase space
- Least action principle in phase space
- Reduced action and Maupertuis' principle
- Canonical transformations
- Liouville's theorem
- Hamilton-Jacobi equations and outlook on quantum mechanics

- Relativistic mechanics
- Relativistic kinematics and Lorentz transformations
- Relativistic dynamics
- Relativistic least action principle

- Continuum mechanics and classical field theory
- Relativistic field theory
- Energy-momentum tensor

- Electrodynamics
- Vector potential and field tenso
- Lagrangian density and equations of motion
- Gauge invariance
- Energy-momentum tensor, energy of fields and matter
- Electromagnetic field in vacuum
- Field generated by a current density
- Potential and field of a point particle
- Radiation of an oscillating charge distribution
- Self-interaction and incompleteness of electrodynamics