Collective coordinate quantization: Relativistic and gauge symmetric aspects

The introduction and quantization of a center-of-mass coordinate is demonstrated for the one-soliton sector of nonlinear field theories in (1+1) dimensions. The present approach strongly emphasizes the gauge and BRST-symmetry aspects of collective coordinate quantization. A gauge is presented which is independent of any approximation scheme and which allows to interpret the new degree of freedom as the quantized center of mass coordinate of a soliton. Lorentz invariance is used from the beginning to introduce fluctuations of the collective coordinate in the rest frame of the moving soliton. It turns out that due to the extended nature of the soliton retardation effects lead to differences in the quantum mechanics of the soliton as compared to a point-like particle. Finally, the results of the semiclassical expansion are used to analyse effective soliton-meson vertices and the coupling to an external source. Such a coupling in general causes acceleration as well as internal excitation of the soliton. (orig.)