Dynamical Symmetries

Abstract

We have seen in the preceding chapters that the symmetry and degeneracy of the states of a system are associated with each other. For example, a system that possesses rotational symmetry is usually degenerate with respect to the direction of the angular momentum, i.e. with respect to the eigenvalues of a particular component (usually J _z ). An exception is the case J = 0. In the case of the discrete symmetries of space-inversion and time-reversal discussed in the previous chapter, degeneracy is less common since the transformed states are quite frequently equal to the original states.