Classical solutions in quantum field theory : solitons and by Erick J. Weinberg

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By Erick J. Weinberg

''Classical options play an enormous function in quantum box idea, high-energy physics, and cosmology. Real-time soliton recommendations supply upward thrust to debris, reminiscent of magnetic monopoles, and prolonged constructions, resembling area partitions and cosmic strings, that experience implications for the cosmology of the early universe. Imaginarytime Euclidean instantons are liable for very important nonperturbative results, while Read more...

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There will be two types of kinks (A-to-B and B-to-C), and two types of antikinks. If a right-moving B-to-C kink collides with a leftmoving C-to-B antikink, the emerging particles may be a right-moving A-to-B kink and a left-moving B-to-A antikink. The analogous behavior in the collision of domain walls separating different (not necessarily degenerate) vacua in four spacetime dimensions leads, in certain theories, to an interesting new possibility, termed classical transitions [22, 23], that are an alternative to the transitions via quantum mechanical bubble nucleation that will be discussed in Chap.

Each two-dimensional kink mode with eigenvalue ω gives rise to a family of modes with frequencies ω 2 + k2T , where kT represents the wavenumbers in the spatial directions parallel to the wall. If the two-dimensional mode was a bound state mode localized about the kink, the D-dimensional mode can be interpreted as a particle of mass ω whose motion is confined to the domain wall. The translational zero mode goes over to a family of massless modes with frequency |k|; these correspond to small deformations of the planar domain wall.

A word of caution is in order. We might well expect that in the strong-coupling regime higher-order quantum corrections would be important, thus rendering both our expression for the kink mass and the WKB result for the breather masses meaningless. However, the results described below suggest that this may not be the case, and that the sine-Gordon theory is sufficiently special that the WKB formula for the mass might be exact, as indeed turns out to be the case [30, 31]. At the same time, though, it should be kept in mind that in the strong-coupling regime the kink Compton wavelength is greater than the classical soliton width and the direct significance of the classical field profile in the quantum state is uncertain.

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