Related papers: Superposition principle and Kirchhoff's integral t…
We challenge the view that there is a basic conflict between the fundamental principles of Quantum Theory and General Relativity, and in particular the fact that a superposition of massive bodies would lead to a violation of the Equivalence…
In this short note, based on Carleman estimates and Holmgren's type theorems, we provide a converse theorem of the classical Huygens principle for free wave equations. Possible generalizations to other underlying space-times or other wave…
The quantum superposition principle is reexamined and reformulated based on the adiabatic theorem of quantum mechanics, nonadiabatic dressed states and experimental evidences. The collapse of the wave function and the quantum measurement…
A hyperplane arrangement is called formal provided all linear dependencies among the defining forms of the hyperplanes are generated by ones corresponding to intersections of codimension two. The significance of this notion stems from the…
Superfilters are generalized ultrafilters, which capture the underlying concept in Ramsey theoretic theorems such as van der Waerden's Theorem. We establish several properties of superfilters, which generalize both Ramsey's Theorem and its…
We study the nonresonance phenomenon for complex rank-one local systems on complements of hyperplane arrangements. We refine the method of Cohen, Dimca, and Orlik and obtain a combinatorial sufficient condition for nonresonance. As an…
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…
We review some applications of self-consistent Green's function theory to studies of one- and two-nucleon structure in finite nuclei. Large-scale microscopic calculations that employ realistic nuclear forces are now possible. Effects of…
We generalize the fundamental structure Theorem on Hopf (bi)-modules by Larson and Sweedler to quasi-Hopf algebras H. If H is finite dimensional this proves the existence and uniqueness (up to scalar multiples) of integrals in H. Among…
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…
The superposition principle is the cornerstone of quantum mechanics, leading to a variety of genuinely quantum effects. Whether the principle applies also to macroscopic systems or, instead, there is a progressive breakdown when moving to…
Several classic problems for particles diffusing outside an arbitrary configuration of non-overlapping partially reactive spherical traps in three dimensions are revisited. For this purpose, we describe the generalized method of separation…
Due to spectral obstructions, a scattering theory in the Lax-Phillips sense for the wave equation for differential p-forms on H^{n+1} cannot be developed. As a consequence, Huygens' principle for the wave equation in this context does not…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
We remind and emphasize the connections and differences between Kirchhoff and Born modelling. We discuss how they lead to a general expression for the conversion of a velocity model perturbation into a reflectivity through the "generalized…
First and second order corrections for the scattering of different types of particles by a weak gravitational field, treated as an external field, are calculated. These computations indicate a violation of the Equivalence Principle: to…
The uncertainty principle suggests a quantitative trade-off between the control of position and the control of momentum in particle propagation. However, a superposition of two states with very different uncertainty trade-offs introduces an…
Although Quantum field theory has been very successful in explaining experiment, there are two aspects of the theory that remain quite troubling. One is the no-interaction result proved in Haag's theorem. The other is the existence of…
Qualitative characteristics and the rigorous definition of a concept of the double symmetry is given. We use some double symmetry for constructing a theory of fields not investigated before which transform as the proper Lorentz group…
First, we point out that the present applied superposition principle is linear, it must be developed into a generality. Next, the linear operators and equations should be developed nonlinearly. They will include nonlinear Klein-Gordon…