Solitons on the Boundaries of Microscopic Systems
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In this chapter, we focus on some applications of soliton theory in microscopic compact systems with boundary, like nuclei or quantum Hall liquids. At this space scale, the solitons correspond to solutions of field equations with finite energy and with a localized, nondispersive energy density. Since the field theories describing many-body systems of elementary particles are quantum theories, one should perform the so-called quantization of solitons procedure. This is done in principle by using a semiclassical expansion to associate with a classical soliton solution both a quantum soliton-particle states, and a whole series of excited state by quantizing the fluctuations around the soliton. Since the soliton solutions are nonperturbative, their quantum versions are themselves nonperturbative [267, 161].