Related papers: Radon Transforms and the SYK model
We study the effects of relative locality dynamics in the case of the Snyder model. Several properties of this model differ from those of the widely studied $\kappa$-Poincar\'e models: for example, in the Snyder case the action of the…
We interpret the setting for a Radon transform as a submanifold of the space of generalized functions, and compute its extrinsic curvature: it is the Hessian composed with the Radon transform.
We investigate the phase space structure of the relativistic Sitnikov problem in the first post-Newtonian approximation. The phase space portraits show a strong dependence on the gravitational radius which describes the strength of the…
We obtain explicit inversion formulas for the Radon-like transform that assigns to a function on the unit sphere the integrals of that function over hemispheres lying in lower dimensional central cross-sections. The results are applied to…
We investigate $T\bar{T}$ deformation on non-Hermitian coupled Sachdev-Ye-Kitaev (SYK) model and the holographic picture. The relationship between ground state and thermofield double state is preserved under the $T\bar{T}$ deformation. We…
We find the transformations from the basis of the hydrogen atom of n-dimensions to the basis of the harmonic oscillator of N=2(n-1) dimensions using the Cayley transformation and the Hurwitz matrices. We prove that the eigenfunctions of the…
System of Majorana zero modes with random infinite range interactions -- the Sachdev-Ye-Kitaev (SYK) model -- is thought to exhibit an intriguing relation to the horizons of extremal black holes in two-dimensional anti-de Sitter (AdS$_2$)…
In this paper, we obtain Pizzetti-type formulae on regions of the the unit sphere $\mathbb{S}^{m-1}$ of $\mathbb{R}^m$, and study their applications to the problem of inverting the spherical Radon transform. In particular, we approach…
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…
The following two inversion methods for Radon-like transforms are widely used in integral geometry and related harmonic analysis. The first method invokes mean value operators in accordance with the classical Funk-Radon-Helgason scheme. The…
We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the…
We entertain the idea that a suitable background of cold (very low momentum) pseudoscalar particles or condensate, may trigger a background that effectively generates Lorentz-invariance violation. This aether-like background induces a…
Stationary solution of one-dimensional Sine-Gordon system is embedded in a multidimensional theory with explicitly finite domain in the added spatial dimensions. Semiclassical corrections to energy are calculated for static kink solution…
We study the limiting behavior of eigenfunctions/eigenvalues of the Laplacian of a family of Riemannian metrics that degenerates on a hypersurface. Our results generalize earlier work concerning the degeneration of hyperbolic surfaces.
We investigate a bosonic variant of the Sachdev-Ye-Kitaev (SYK) model coupled to a Lindbladian environment, focusing on the interplay between quantum many-body dynamics and dissipation. Using the Schwinger-Keldysh path integral formalism in…
This is a continuation of a series of papers [FL1, FL2, FL3], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we continue to study the…
Analogous to Weil-Petersson quasicircles, we investigate infinite circle patterns in the Euclidean plane parameterized by discrete harmonic functions of finite Dirichlet energy. The space of such circle patterns forms an…
This article surveys recent results aiming at obtaining refined mapping estimates for the X-ray transform on a Riemannian manifold with boundary, which leverage the condition that the boundary be strictly geodesically convex. These…
Using the sine-Gordon model as the prime example an alternative approach to integrable boundary conditions for a theory restricted to a half-line is proposed. The main idea is to explore the consequences of taking into account the…
We consider the weighted Radon transforms $R_W$ along hyperplanes in $R^d, \, d \geq 3$, with strictly positive weights $W = W (x, \theta), \, x \in R^d, \, \theta \in S^{d-1}$. We construct an example of such a transform with non-trivial…