Related papers: Localization in Nets of Standard Spaces

A novel reduction procedure for covariant classical field theories, reflecting the generalized symplectic reduction theory of Hamiltonian systems, is presented. The departure point of this reduction procedure consists in the choice of a…

The theoretical basis of the phenomenon of effective and exact dimensional reduction, or holographic correspondence, is investigated in a wide variety of physical systems. We first derive general inequalities linking quantum systems of…

Inspired by Bohr's dictum that "physical phenomena are observed relative to different experimental setups", this article investigates the notion of relativity in Bohr's sense, starting from a set of binary elements. The most general form of…

We formulate conformal field theory in the setting of algebraic quantum field theory as Haag-Kastler nets of local observable algebras with diffeomorphism covariance on the two-dimensional Minkowski space. We then obtain a decomposition of…

Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of exponential objects provided by continuous convergence. In this…

We classify Haag-dual Poincar\'e covariant subsystems $\B\subset \F$ of a graded-local net $\F$ on 4D Minkowski spacetime which satisfies standard assumptions and has trivial superselection structure. The result applies to the canonical…

Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…

We develop the theoretical foundations of a generalized Gromov-Hausdorff distance between functions on networks that has recently been applied to various subfields of topological data analysis and optimal transport. These functional…

For any graph, we define a rank-1 operator on a bipartite tensor product space, with components associated to the set of vertices and edges respectively. We show that the partial traces of the operator are the Laplacian and the…

We consider the entanglement entropy for a spacetime region and its spacelike complement in the framework of algebraic quantum field theory. For a M\"obius covariant local net satisfying a certain nuclearity property, we consider the von…

We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…

In this paper we propose a space-time random tensor network approach for understanding holographic duality. Using tensor networks with random link projections, we define boundary theories with interesting holographic properties, such as the…

We present a classification, up to isomorphisms, of all the homogeneous spaces of the Lorentz group with dimension lower than six. At the same time, we classify, up to conjugation, all the non-discrete closed subgroup of the Lorentz group…

We consider the sensor network localization problem, which is closely related to multidimensional scaling and Euclidean distance matrix completion. Given a ground truth configuration of $n$ points in $\mathbb{R}^\ell$, we observe a subset…

Both the additional non-linear term in the Schr\"odinger equation and the additional non-Hamiltonian term in the von Neumann equation, proposed to ensure localisation and decoherence of macro-objects, resp., contain the same Newtonian…

As a novel approach with possible relevance to semiclassical gravity, we propose to define regions of space as quantum subsystems. After recalling how to divide a generic quantum system into ``parts'', we apply this idea to a free scalar…

We introduce the notion of virtual endomorphisms of Lie algebras and use it as an approach for constructing self-similarity of Lie algebras. This is done in particular for a class of metabelian Lie algebras having homological type F Pn,…

We generalise the inference procedure for eigenvectors of symmetrizable matrices of Tyler (1981) to that of invariant and singular subspaces of non-diagonalizable matrices. Wald tests for invariant vectors and $t$-tests for their individual…

We challenge the widespread belief, originated by Newton and Wigner (Rev. Mod. Phys, 21, 400 (1949)) that the incorporation of special relativity into quantum mechanics implies that a massive particle cannot be localized within an…

Learning node representations is a fundamental problem in graph machine learning. While existing embedding methods effectively preserve local similarity measures, they often fail to capture global functions like graph distances. Inspired by…