Uniform semiclassical trace formula for U(3) -> SO(3) symmetry breaking
We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term 1/4 epsilon r(4). This term breaks the U(3) symmetry of the HO, resulting in a spherical system with SO(3) symmetry. We first treat the anharmonic term for small e in semiclassical perturbation theory by integration of the action of the perturbed
