lecture25: conservation laws and Noether's theorem

Topics covered

• Hamilton's principle
• Conservation laws
• Conservation law example
• Several independent variables
• Conservation laws
• Variational symmetries
• Jacobian
• Example transformations
• Transformation of a function
• Transform invariance
• Infinitesimal generators
• Examples
• Emmy Noether
• Noether's theorem %
• Sketch proof
• Example (i)
• Example (ii) %
• Example (iii)
• More than one dependent variable
• Example: rotations
• Common symmetries
• Finding symmetries
• More advanced cases %
• Finding variational symmetries %
• Fields and conservation of charge