Double-delta potentials: one dimensional scattering. The Casimir effect and kink fluctuations

Details Double-delta potentials: one dimensional scattering. The Casimir effect and kink fluctuations Double-delta potentials: one dimensional scattering. The Casimir effect and kink fluctuations

2010-10-15

arxiv.org/abs/1010.3116v3

Int.J.Theor.Phys.50:2227-2241,2011

Physics

Mathematical Physics

15 pages. To be published in the International Journal of Theoretical Physics

Scientific paper

10.1007/s10773-011-0723-0

The path is explored between one-dimensional scattering through Dirac-$\delta$ walls and one-dimensional quantum field theories defined on a finite length interval with Dirichlet boundary conditions. It is found that two $\delta$'s are related to the Casimir effect whereas two $\delta$'s plus the first transparent P$\ddot{\rm o}$sch-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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