Domain wall interactions due to vacuum Dirac field fluctuations in 2+1 dimensions

Abstract

We evaluate quantum effects due to a $2$-component Dirac field in $2+1$ space-time dimensions, coupled to domain-wall like defects with a smooth shape. We show that those effects induce non trivial contributions to the (shape-dependent) energy of the domain walls. For a single defect, we study the divergences in the corresponding self-energy, and also consider the role of the massless zero mode, corresponding to the Callan-Harvey mechanism, by coupling the Dirac field to an external gauge field. For two defects, we show that the Dirac field induces a non trivial, Casimir-like effect between them, and provide an exact expression for that interaction in the case of two straight-line parallel defects. As is the case for the Casimir interaction energy, the result is finite and unambiguous.

17 pages, 1 figure

References in corpus (5)

• Casimir forces in a T operator approach
• Quantum vacuum energies and Casimir forces between partially transparent $\delta$-function plates
• Geometrical and topological aspects of graphene and related materials
• Functional approach to the fermionic Casimir effect
• Quantum vacuum interaction between two sine-Gordon kinks