Interactions between delta-like sources and potentials

Abstract

The modified scalar boson propagator due to the presence of a hyperplane semi-transparent mirror is computed. From this, the classical interaction between static charges and the mirror is investigated employing delta-like potentials and sources. Although the calculations for hyperplane mirrors are performed in arbitrary dimensions, and in a completely general way, it is shown that the results give rise to the usual image method as a particular case. The interaction between a point-like mirror and a point-like source is also considered in $3+1$ dimensions, where a central $1/R^2$ attractive potential is also obtained as a special case.

8 pages, 1 figure

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• Mirrors and field sources in a Lorentz-violating scalar field theory
• Magnetoelectric boundary simulated by a Chern-Simons-like model
• Quasi-local Casimir energy and vacuum buoyancy in a weak gravitational field
• Features of planar Lee-Wick electrodynamics
• Material boundaries in Carroll-Field-Jackiw Lorentz-violating electrodynamics
• Dirichlet boundary condition for the Lee-Wick-like scalar model
• Semi-transparent boundaries in CPT-even Lorentz violating electrodynamics
• The role of scalar current coupling along surfaces
• One-dimensional scattering of fermions in double Dirac delta potentials
• A Two-Gauge Field Model for Magnetoelectric Boundaries
• Generalized Neumann boundary condition for the scalar field