Related papers: Operator Spin Foam Models
Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group…
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
We introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry…
We study the higher spin anologs of the six vertex model on the basis of its symmetry under the quantum affine algebra $U_q(\slth)$. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer…
We provide an algorithm to estimate the divergence degree of the Lorentzian EPRL-FK spin foam amplitudes for arbitrary 2-complexes. We focus on the "self-energy" and "vertex renormalization" diagrams and find an upper bound estimate. We…
Numerical methods are a powerful tool for doing calculations in spinfoam theory. We review the major frameworks available, their definition, and various applications. We start from $\texttt{sl2cfoam-next}$, the state-of-the-art library to…
Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…
Spin foams arose as the covariant (path integral) formulation of quantum gravity depicting transition amplitudes between different quantum geometry states. As such, they provide a scheme to study the no boundary proposal, specifically the…
A spin space group provides a suitable way to fully exploit the symmetry of a spin arrangement with a negligible spin-orbit coupling. There has been a growing interest in applying spin symmetry analysis with the spin space group in the…
Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group…
We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply Migdal-Kadanoff and Tensor Network…
We present an algorithm which determines the fundamental group of a spatial section using topspin networks. Tracking the topology of the spatial section is a unique feature of this approach, which is not possible in standard Loop Quantum…
The Schwinger boson theory provides a natural path for treating quantum spin systems with large quantum fluctuations. In contrast to semi-classical treatments, this theory allows us to describe a continuous transition between magnetically…
Effective spin foams provide the computationally most efficient spin foam models yet and are therefore ideally suited for applications e.g. to quantum cosmology. We provide here the first effective spin foam computations of a finite time…
We present formulations and numerical algorithms for solving diffeomorphic shape matching problems. We formulate shape matching as a variational problem governed by a dynamical system that models the flow of diffeomorphism $f_t \in…
The widespread success of foundation models in natural language processing and computer vision has inspired researchers to extend the concept to scientific machine learning and computational science. However, this position paper argues that…
The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new…
Safe real-time control of robotic manipulators in unstructured environments requires handling numerous safety constraints without compromising task performance. Traditional approaches, such as artificial potential fields (APFs), suffer from…
Tried-and-true flapping wing robot simulation is essential in developing flapping wing mechanisms and algorithms. This paper presents a novel application-oriented flapping wing platform, highly compatible with various mechanical designs and…