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Related papers: Holography on local fields via Radon Transform

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We introduce and study a new Radon-like transform that averages projected differential p-forms in R^n over affine (n-k)-planes. We then prove an explicit inversion formula for our transform on the space of rapidly-decaying smooth p-forms.…

Differential Geometry · Mathematics 2009-08-21 Bruce Solomon

High-dimensional Hilbert spaces possess large information encoding and transmission capabilities. Characterizing exactly the real potential of high-dimensional entangled systems is a cornerstone of tomography and quantum imaging. The…

Quantum Physics · Physics 2017-10-10 Laszlo Gyongyosi

We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…

Analysis of PDEs · Mathematics 2015-09-02 Leonid Kunyansky

In this article we explore the holographic approach to neutron stars in the realm of Quantum Field Theory (QFT). We delve into the structures of neutron stars, emphasizing the application of the AdS/CFT duality in modeling them. We discuss…

High Energy Physics - Theory · Physics 2024-01-04 Tinglong Feng

Hyperplane is a set of non-injectivity of the spherical Radon transform (SRT) in the space of continuous functions in R^d. In this article, for the reconstruction of an unknown function f from C(R^3) (the support can be non-compact), using…

Classical Analysis and ODEs · Mathematics 2024-04-09 Rafik Aramyan

We construct a gravitational dual of the pseudo-conformal universe, a proposed alternative to inflation in which a conformal field theory in nearly flat space develops a time dependent vacuum expectation value. Constructing this dual…

High Energy Physics - Theory · Physics 2015-02-02 Kurt Hinterbichler , James Stokes , Mark Trodden

The standard Radon transform of holomorphic functions is not always well defined, as the integration of such functions over planes may not converge. In this paper, we introduce new Radon-type transforms of co-(real)dimension $2$ for…

Complex Variables · Mathematics 2025-09-10 Ren Hu , Pan Lian

We write the spherical curl transformation for Trkalian fields using differential forms. Then we consider Radon transform of these fields. The Radon transform of a Trkalian field satisfies a corresponding eigenvalue equation on a sphere in…

Mathematical Physics · Physics 2014-11-20 K. Saygili

We propose that general D-dimensional quantum field theories are dual to (D+1)-dimensional local quantum theories which in general include objects with spin two or higher. Using a general prescription, we construct a (D+1)-dimensional…

High Energy Physics - Theory · Physics 2010-04-23 Sung-Sik Lee

The Radon transform is a fundamental tool for analyzing data in tomographic imaging, optimal transport, crystallography, and geometric analysis. Numerical computations require an accurate discretization. To deal with voxelized images and…

Numerical Analysis · Mathematics 2026-03-17 Robert Beinert , Jonas Bresch , Michael Quellmalz

We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In $\mathbb{R}^3$ it maps a function to its surface integrals over circular cones, and in $\mathbb{R}^2$ it maps a function to its…

Numerical Analysis · Mathematics 2015-06-17 Rim Gouia-Zarrad , Gaik Ambartsoumian

We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and study some of their properties. In particular we obtain a support theorem that generalizes Helgason's support theorem for…

Representation Theory · Mathematics 2013-04-04 J. J. Kuit

The Radon transform is a linear integral transform that mimics the data formation process in medical imaging modalities like X-ray Computerized Tomography and Positron Emission Tomography. The Hough transform is a pattern recognition…

Numerical Analysis · Mathematics 2016-05-31 Riccardo Aramini , Fabrice Delbary , Mauro C. Beltrametti , Michele Piana , Anna Maria Massone

Recovering a function from its integrals over circular cones recently gained significance because of its relevance to novel medical imaging technologies such emission tomography using Compton cameras. In this paper we investigate the case…

Numerical Analysis · Mathematics 2016-06-14 Daniela Schiefeneder , Markus Haltmeier

High-dimensional biphoton states are promising resources for quantum applications, ranging from high-dimensional quantum communications to quantum imaging. A pivotal task is fully characterising these states, which is generally…

Quantum Physics · Physics 2023-02-20 Danilo Zia , Nazanin Dehghan , Alessio D'Errico , Fabio Sciarrino , Ebrahim Karimi

Using the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of $\mathrm{AdS}_3/\mathrm{CFT}_2$. We find that, given…

High Energy Physics - Theory · Physics 2020-12-30 ChunJun Cao , Xiao-Liang Qi , Brian Swingle , Eugene Tang

Currently, theory of ray transforms of vector and tensor fields is well developed, but the Radon transforms of such fields have not been fully analyzed. We thus consider linearly weighted and unweighted longitudinal and transversal Radon…

Analysis of PDEs · Mathematics 2023-05-24 L. Kunyansky , E. McDugald , B. Shearer

We explain how to relate the ideas of Carroll geometry, matrix theory on instantonic objects, and infinite boost limits of M-theory. Based on these new insights, we explore the implications for possible holographic constructions involving a…

High Energy Physics - Theory · Physics 2026-02-23 Chris D. A. Blair , Niels A. Obers , Ziqi Yan

We define a new integral transform on the real sphere which is invariant relative to the orthogonal group and similar to the horospherical Radon transform for the hyperbolic space. This transform involves complex geometry associated with…

Representation Theory · Mathematics 2007-05-23 Simon Gindikin

We obtain new inversion formulas for the Radon transform and the corresponding dual transform acting on affine Grassmann manifolds of planes in $R^n$. The consideration is performed in full generality on continuous functions and functions…

Functional Analysis · Mathematics 2016-10-10 Boris Rubin , Yingzhan Wang