Related papers: Comments on the radial plane waves
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
Using the spectral properties of orthogonal polynomials, we introduce a finite version of quantum field theory for elementary particles. Closed-loop integrals in the Feynman diagrams for computing transition amplitudes are finite.…
The existence of phase resonances in obliquely illuminated, perfectly conducting compound gratings is investigated. The diffraction problem of a p-polarized plane wave impinging on the structure is solved using the modal approach. The…
We consider space-times with two isometries which represent gravitational waves with distinct wavefronts which propagate into exact Friedmann-Robertson-Walker (FRW) universes. The geometry of possible wavefronts is analysed in detail in all…
The concepts of Feynman integrals in white noise analysis are used to construct the Feynman integrand for the harmonic oscillator in momentum space representation as a Hida distribution. Moreover it is shown that in a limit sense, the…
A formula to investigate wave effect in multi-lens system is presented on the basis of path integral formalism by generalizing the work by Nakamura and Deguchi (1999). Wave effect of a system with two lenses is investigated in an analytic…
Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…
The idealization of monochromatic plane waves leads to considerable simplifications in the analysis of electromagnetic systems. However, for active systems this idealization may be dangerous due to the presence of growing waves. Here we…
Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in…
From the measurement of a reflection spectrum of an open microwave cavity the poles of the scattering matrix in the complex plane have been determined. The resonances have been extracted by means of the harmonic inversion method. By this it…
The ``spatial interpretation of compositeness'', presented and discussed in [1,2] in the context of non-relativistic potential scattering, is extended to higher partial waves. A particular set of basis states is used to arrive at a slightly…
The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the…
In recent years a lot of attention has been paid to topological spaces which are a bit more general than smooth manifolds - orbifolds. Orbifolds are intuitively speaking manifolds with some singularities. The formal definition is also…
We consider a time-harmonic wave problem, appearing for example in water-waves and in acoustics, in a setting such that the analysis reduces to the study of a 2D waveguide problem with a Neumann boundary condition. The geometry is symmetric…
We derive two methods for simultaneously controlling the resonance frequency, linewidth and multipolar nature of the resonances of radially symmetric structures. Firstly, we formulate an eigenvalue problem for a global shift in the…
We show that certain iteration systems lead to fractal measures admitting exact orthogonal harmonic analysis.
Sufficient conditions for wave breaking are found for the short-pulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of characteristics and conserved quantities of the…
A new method is developed for solving the conformally invariant integrals that arise in conformal field theories with a boundary. The presence of a boundary makes previous techniques for theories without a boundary less suitable. The method…
A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for…
It is proved that one can choose a control function on an arbitrary small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number…