New look at the zero-mode problem of kink translations

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Abstract
In the semiclassical approximation to a one-dimensional quantum field theory with a double-well potential one has to consider also the quantum oscillations about the kink solution. Because of the continuous translation parameter of the kink, there are nonharmonic oscillations which naively give a diverging contribution. This, the so-called zero-mode problem, is usually handled by the collective-coordinate method. I show that when the Gaussian approximation to the integrand is done with sufficient care, there will be no zero-mode problem when the path integral is eventually evaluated.