ABSTRACT
In particle physics, fundamental symmetries are revealed not so much in terms of shape or physical structure, or even in terms of the motions of particular objects or systems. The variational principle is a very powerful principle – it implies that equations of motion governing a system are determined by extremization of a scalar functional. It generalizes to quantum mechanics, general relativity and quantum field theory. For every symmetry of the action there is a conservation law which is called Noether’s theorem, obtained by Emmy Noether in 1917. The foundational symmetries of particle physics are spacetime symmetries: symmetries that transform the coordinates of space and time. Time-translation will be a symmetry of any system whose Lagrangian does not explicitly depend on the time coordinate.
