Related papers: On spectral representations of tensor random field…
It has recently been shown that there exists a class of stable gapless spin liquids in 3+1 dimensions described by higher rank tensor U(1) gauge fields, giving rise to an emergent tensor electromagnetism. The tensor gauge field of these…
This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a…
Let V be an n-dimensional vector space and let On be the orthogonal group. Motivated by a question of B. Szegedy (B. Szegedy, Edge coloring models and reflection positivity, Journal of the American Mathematical Society Volume 20, Number 4,…
Different sequences of ellipsoids are represented on the ellipticity-rotation plane. The rotation parameter is defined as the ratio of kinetic energy related to the mean tangential equatorial velocity component to kinetic energy related to…
We investigate the relationship between ergodicity and asymptotic Gaussianity of isotropic spherical random fields, in the high-resolution (or high-frequency) limit. In particular, our results suggest that under a wide variety of…
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…
This Thesis presents some physically motivated criteria for the existence of particles and infra-particles in a given quantum field theory. It is based on a refined spectral theory of automorphism groups describing the energy-momentum…
Motivated by phenomenological questions in quantum gravity, we consider the propagation of a scalar field on a random lattice. We describe a procedure to calculate the dispersion relation for the field by taking a limit of a periodic…
We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale…
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…
We consider the universal part of entanglement entropy across a plane in flat space for a QFT, giving a non-perturbative expression in terms of a spectral function. We study the change in entanglement entropy under a deformation by a…
Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher…
Tensor ring (TR) decomposition is an efficient approach to discover the hidden low-rank patterns for higher-order tensors, and streaming tensors are becoming highly prevalent in real-world applications. In this paper, we investigate how to…
Macroscopic fields like electromagnetic, MHD, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the interacting boson model. A mean-field analysis links different regions of the parameter space with definite geometric shapes.…
Gaussian random fields are among the most important models of amorphous spatial structures and appear across length scales in a variety of physical, biological, and geological applications, from composite materials to geospatial data.…
We consider the slowly rotating relativistic stars with a uniform angular velocity in the scalar-tensor gravity, and examine the rotational effect around such compact objects. For this purpose, we derive a 2nd order differential equation…
Making use of the real sl(2,R) Lie group algebra generating a spin 1/2 Lie group allows to create an explicitly given Lorentz invariant fermion wave. As the generators are real valued they can be interpreted as a deformation tensor in…
The association of all three soft gamma-ray repeaters (SGRs) with supernova remnants has made possible estimates of the distance to and luminosity of the sources of SGRs, which have provided a starting point for detailed modeling. One of…
Tensor models are measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as additionally to the…