Symmetry and Collective Dynamics
Abstract. Emmy Noether’s famous theorem (1918) is a cornerstone of theoretical physics. The theorem states that every smooth invertible symmetry of the Lagrangian in Hamil- ton?s variational principle is associated with a conservation law. For example, momentum and energy are conserved, respectively, for invariance under space and time translations. Another example is the conservation of angular momentum for Lagrangians that are in- variant under rotations. We will explain how the symmetry transformations in Noether?s theorem specify the optimal variables for expressing collective dynamics and derive their equations.
This will be a blackboard talk. I will draw the figure below and explain it, step-by-step.