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

Abstract

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$\ddot{\mathrm{o}}$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.

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

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Cited by in corpus (15)

• Quantum vacuum energies and Casimir forces between partially transparent $\delta$-function plates
• Two-point one-dimensional $\delta$-${\delta }^{\prime }$ interactions: non-abelian addition law and decoupling limit
• QFT over the finite line. Heat kernel coefficients, spectral zeta functions and selfadjoint extensions
• One-loop kink mass shifts: a computational approach
• Capturing non-exponential dynamics in the presence of two decay channels
• Point interactions with bias potentials
• Quantum field theories with boundaries and novel instabilities
• Analysis of a one-dimensional Hamiltonian with a singular double well consisting of two nonlocal ${\delta }^{\prime }$ interactions
• Free energy and entropy for finite temperature quantum field theory under the influence of periodic backgrounds
• Fermionic edge states and new physics
• Scattering data and bound states of a squeezed double-layer structure
• Modelling quantum black hole
• One-dimensional scattering of fermions in double Dirac delta potentials
• Casimir energy through transfer operators for sine-Gordon backgrounds
• Quantum field theory at finite temperature for 3D periodic backgrounds