Second order theory of excitations in trapped bose condensates at finite temperatures

We present a finite temperature field theory for collective excitations of trapped Bose condensates which includes the dynamics of the thermal cloud. In spherical traps we show that excitations couple strongly to a small number of modes, giving resonance structure in their frequency spectra. Where possible, we derive energy shifts and lifetimes of excitations. For the l = 0 mode we show that the simple picture of a decay rate fails, which should be observable in suitable experiments. It also suggests a possible explanation for the anomalous behavior of the m = 0 mode observed in anisotropic traps.