Casimir energy through transfer operators for sine-Gordon backgrounds

Abstract

The quantum vacuum interaction energy between a pair of semitransparent two-dimensional plates represented by Dirac delta potentials and its first derivative, embedded in the topological background of a sine-Gordon kink, is studied through an extension of the TGTG-formula (developped by O. Kenneth and I. Klich in the scattering approach). Quantum vacuum oscillations around the sine-Gordon kink solutions are interpreted as a quantum scalar field theory in the spacetime of a domain wall. Moreover, the relation between the phase shift and the density of states (the well-known Dashen-Hasslacher-Neveu formula) is also exploited to characterize the quantum vacuum energy.

28 pages, 4 figures. Version 3 (published version) includes additional comments in appendix A and a change of title. Progress of Theoretical and Experimental Physics, 2024

References in corpus (7)

• Casimir forces in a T operator approach
• Gravitational Casimir effect
• $\delta -{\delta }^{\prime }$ generalized Robin boundary conditions and quantum vacuum fluctuations
• Double-delta potentials: one dimensional scattering. The Casimir effect and kink fluctuations
• Gravitational and Inertial Mass of Casimir Energy
• Monoatomically thin polarizable sheets
• Derivative expansion for the boundary interaction terms in the Casimir effect: generalized $\delta$-potentials