A scalar potential formulation and translation theory for the time-harmonic Maxwell equations

We develop a computational method based on a scalar potential representation, which efficiently reduces the solution of Maxwell’s equations to the solution of two scalar Helmholtz equations. One of the key contributions of this paper is a theory for the translation of Maxwell solutions using such a representation, since the scalar potential form is not invariant with respect to translations. The translation theory is developed by introducing “conversion” operators, which enable the representation of the electric and magnetic vector fields via scalar potentials in an arbitrary reference frame. Advantages of this representation include the fact that only two Helmholtz equations need be solved, and moreover, the divergence free constraints are satisfied automatically, by construction. The availability of a translation theory for this representation can find application in methods such as the Fast Multipole Method. For illustration of the use of the representation and translation theory we implemented an algorithm for the simulation of Mie scattering off a system of spherical objects of different sizes and dielectric properties using a variant of the T-matrix method. The resulting system was solved using an iterative method based on GMRES. The results of the computations agree well with previous computational and experimental results

Post-Newtonian Approximation in Maxwell-Like Form

The equations of the linearized first post-Newtonian approximation to general relativity are often written in "gravitoelectromagnetic" Maxwell-like form, since that facilitates physical intuition. Damour, Soffel and Xu (DSX) (as a side issue in their complex but elegant papers on relativistic celestial mechanics) have expressed the first post-Newtonian approximation, including all nonlinearities, in Maxwell-like form. This paper summarizes that DSX Maxwell-like formalism (which is not easily extracted from their celestial mechanics papers), and then extends it to include the post-Newtonian (Landau-Lifshitz-based) gravitational momentum density, momentum flux (i.e. gravitational stress tensor) and law of momentum conservation in Maxwell-like form. The authors and their colleagues have found these Maxwell-like momentum tools useful for developing physical intuition into numerical-relativity simulations of compact binaries with spin.Comment: v4: Revised for resubmission to Phys Rev D, 6 pages. v3: Reformulated in terms of DSX papers. Submitted to Phys Rev D, 6 pages. v2: Added references. Changed definitions & convention

3D heterotic string theory: new approach and extremal solutions

We develop a new formalism for the bosonic sector of low-energy heterotic string theory toroidally compactified to three dimensions. This formalism is based on the use of some single non-quadratic real matrix potential which transforms linearly under the action of subgroup of the three-dimensional charging symmetries. We formulate a new charging symmetry invariant approach for the symmetry generation and straightforward construction of asymptotically flat solutions. Finally, using the developed approach and the established formal analogy between the heterotic and Einstein-Maxwell theories, we construct a general class of the heterotic string theory extremal solutions of the Israel-Wilson-Perjes type. This class is asymptotically flat and charging symmetry complete; it includes the extremal solutions constructed before and possesses the non-trivial bosonic string theory limit.Comment: 20 pages in Late