Path-integral approach to electromagnetic phenomena in inhomogeneous systems

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We derive a path-integral expression for the time-evolution operator associated with the Maxwell’s equations in an inhomogeneous medium and show that its asymptotic behavior for large light velocity corresponds to geometrical optics. We also describe a path-integral approach to the solution of the Laplace equation in an inhomogeneous medium. This approach leads to new numerical methods for the solution of Laplace and Poisson equations in inhomogeneous media of irregular shape. An expression for the image potential near a surface with continuously changing dielectric function is also derived.