Scattering of time-harmonic electromagnetic waves by penetrable, anisotropic dielectric obstacles admits an equivalent formulation in terms a strongly singular volume integral equation (VIE). The aim this study is to analyse the essential spectrum operator that describes case where permittivity piecewise constant symmetric $$3\times 3$$ matrix with some bounds on eigenvalues. For Lipschitz inte...

Here the path integral is over real metrics modulo coordinate transformations, G denotes a renormalized Newton constant and the · · · indicate higher derivative terms like R, etc. There may also be nonlocal terms related to the conformal anomaly [2]. The integral over μ produces the volume fixing delta function δ( ∫ dx √ g − V ). If this integral were done in the saddle point approximation, the...