Related papers: Fourier Calculus from Intersection Theory
A variational formulation for the calculation of interacting fermion systems based on the density-matrix functional theory is presented. Our formalism provides for a natural integration of explicit many-particle effects into standard…
The development of accurate and fast numerical schemes for the five fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres…
The dynamic structure factor (DSF) is a mathematical function that contains information about inter-particle correlations and their time evolution. Mostly the classical molecular dynamics is used to calculate the DSF of the classical…
We derive the Boltzmann equation for scalar fields using the Schwinger-Keldysh formalism. The focus lies on the derivation of the collision term. We show that the relevant self-energy diagrams have a factorization property. The collision…
Dimensionally-regulated Feynman integrals are a cornerstone of all perturbative computations in quantum field theory. They are known to exhibit a rich mathematical structure, which has led to the development of powerful new techniques for…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
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…
We present explicit formulas for the intersection pairing in the intersection cohomology of the moduli space $M_0(r)$ of rank-$r$, degree-$0$ semistable bundles on a Riemann surface. The key idea is to realize this intersection cohomology…
Recent work shows that density functional theory calculations accurately describe materials exhibiting turbostratic disorder between layers of incommensurate constituents. These calculations approximate one of the constituents as a finite…
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
This is a review of the program we started in 1968 to understand and generalize Bjorken scaling and Feynman's parton model in a canonical quantum field theory. It is shown that the parton model proposed for deep inelastic electron…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
We deal with the complete-intersection property of maximally differential ideals. Also, we connect the Gorenstein homology of derivations to the Gorenstein property of the base rings. These equipped with some applications.
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
Inhomogeneous polymers play an important role in various cellular processes, both in nature and in biotechnological applications. At finite temperatures, inhomogeneous polymers exhibit non-trivial thermal fluctuations. In a broader context,…
We consider integrals of spherical harmonics with Fourier exponents on the sphere $S^n ,\, n \geq 1$. Such transforms arise in the framework of the theory of weighted Radon transforms and vector diffraction in electromagnetic fields theory.…
We continue our study of scattering theory and dispersive properties for one-dimensional charge transfer models, namely linear Schr\"odinger equations with multiple moving potentials. By the discovery of a refined structure of the…
We uncover a combinatorial structure governing the differential equations satisfied by wavefunction coefficients of scalar fields with generic masses in de Sitter space. Using an integral representation of the massive mode functions, we…
We highlight the important role of the Fourier transform in deriving inversion formulas for the integral transforms of tomographic imaging. We demonstrate this principle by deriving inversion formulas for the divergent beam transform and…
Fourier analysis on the discrete hypercubes $\{-1,1\}^n$ has found numerous applications in learning theory. A recent breakthrough involves the use of a classical result from Fourier analysis, the Bohnenblust--Hille inequality, in the…