Abstract
The path is explored between one-dimensional scattering through Dirac-δ walls and one-dimensional quantum field theories defined on a finite length interval with Dirichlet boundary conditions. It is found that two δ’s are related to the Casimir effect whereas two δ’s plus the first transparent Pösch-Teller well arise in the context of the sine-Gordon kink fluctuations, both phenomena subjected to Dirichlet boundary conditions. One or two delta wells will be also explored in order to describe absorbent plates, even though the wells lead to non unitary Quantum Field Theories.
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The authors thank, M. Asorey and I. Cavero for fruitful observations and conversations. JMG thanks to the Spanish Ministerio de Educación y Ciencia and Junta de Castilla y León for partial financial support under grants FIS2009-10546 and GR224. JMMC thanks the CASIMIR Network (European Science Foundation) and the German Science Foundation (DFG) for partial financial support, as well as M. Bordag for his interest and illuminating conversations.
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Guilarte, J.M., Muñoz-Castañeda, J.M. Double-Delta Potentials: One Dimensional Scattering. Int J Theor Phys 50, 2227–2241 (2011). https://doi.org/10.1007/s10773-011-0723-0
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DOI: https://doi.org/10.1007/s10773-011-0723-0