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The Mishchenko-Fomenko theorem on superintegrable Hamiltonian systems is generalized to superintegrable Hamiltonian systems with noncompact invariant submanifolds. It is formulated in the case of globally superintegrable Hamiltonian systems…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
The wave-function-matching (WFM) technique for first-principles transport-property calculations was modified by S\o{}rensen {\it et al.} so as to exclude rapidly decreasing evanescent waves [S\o{}rensen {\it et al.}, Phys. Rev. B {\bf 77},…
Berry and Klein (J. Mod. Opt. (1997) 43 2139-2164) showed that the Talbot effects in classical optics are naturally explained by Gauss sums studied in number theory. Their result was based on Helmholtz equation. In this article, we explain…
In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…
The Green's function formalism in Condensed Matter Physics is reviewed within the equation of motion approach. Composite operators and their Green's functions naturally appear as building blocks of generalized perturbative approaches and…
The famous equivalence theorem is reexamined in order to make it applicable to the case of intrinsically quantum infinite-component effective theories. We slightly modify the formulation of this theorem and prove it basing on the notion of…
We show how to use the Hopf algebra structure of quantum field theory to derive nonperturbative results for the short-distance singular sector of a renormalizable quantum field theory in a simple but generic example. We discuss renormalized…
In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…
For the complement of a hyperplane arrangement we construct a dual homology basis to the no broken circuit basis of cohomology. This is based on the theory of wonderful embeddings and nested sets.
According to symmetrization postulate for a system of identical particles, wave function has to be completely symmetric or completely anti-symmetric. In this paper we want to mathematically justify this postulate ignoring the spin part of…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann,…
Here we obtain alternative descriptions of massive spin-2 particles by an embedding procedure of the Fierz-Pauli equations of motion. All models are free of ghosts at quadratic level although most of them are of higher order in derivatives.…
A set of curved beams and shells is geometrically implied by level sets of a scalar function over some bulk domain. The mechanical model for each structure is based on the Kirchhoff--Love theory, that is, small displacements without shear…
This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…
The inner structure of the {\gamma}{\epsilon}-formalisms of Infeld and van der Waerden admits the occurrence of spin-tensor electromagnetic fields which bear invariance under the action of the generalized Weyl gauge group. A concise…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
The Green--Griffiths--Lang and Kobayashi hyperbolicity conjectures for generic hypersurfaces of polynomial degree are proved using intersection theory for non-reductive geometric invariant theoretic quotients and recent work of Riedl and…
We construct a Schwinger-Keldysh effective field theory for relativistic hydrodynamics for charged matter in a thermal background using a superspace formalism. Superspace allows us to efficiently impose the symmetries of the problem and to…