Symmetry principles in particle physics

Our purpose in these lectures will be to provide a general introduction to the role played by considerations of invariance, and to discuss the extent to which they may determine the laws of physics. In classical mechanics, the Hamiltonian equations of motion, !> ü1c > (0 tell us that any dynamical variable £, which has a vanishing Poisson bracket with the Hamiltonian, is a constant < are canonically conjugate variables, with the Hamiltonian, is a constant of motion· In particular, if q and p £r Er' S 3H . . j£- ' (2) so that if the Hamiltonian is independent of any particular co-ordinate, the corresponding canonical "momentum" is constant in time· Moreover, one may show that p is the generator of infinitesimal canonical transformations —r which induce transformations of q alone· Thus a problem in classical mechanics, which is completely solved when one has found all the constants of motion» reduces to the problem of finding the generating functions of all infinitesimal transformations which leave the Hamiltonian invariant.