相关论文: Universal homogeneous causal sets

A global representation is a compatible collection of representations of the outer automorphism groups of the groups belonging to some collection of finite groups $\mathscr{U}$. Global representations assemble into an abelian category…

For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some…

General Relativity traces the evolution of our Universe back to a Big Bang singularity. To probe physics before the singularity -- if indeed there is a ``before'' -- we must turn to quantum gravity. The Causal Set approach to quantum…

A subset of a topological space is said to be \emph{universally measurable} if it is measured by the completion of each countably additive $\sigma$-finite Borel measure on the space, and \emph{universally null} if it has measure zero for…

A homogeneous family of subsets over a given set is one with a very ``rich'' automorphism group. We prove the existence of a bi-universal element in the class of homogeneous families over a given infinite set and give an explicit…

We show that there is a countable universal abelian p-group for purity, i.e., a countable abelian p-group $U$ such that every countable abelian p-group purely embeds in $U$. This is the last result needed to provide a complete solution to…

Based on the recent work \cite{PII} we put forward a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations,…

Recent developments in the formalisation of quantum causal structures have made it possible to test and compare hypotheses about causal structure empirically, rather than being a-priori assumptions. Such differences in causal structure may…

We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in metric measure spaces homogeneous with respect to a group acting by measure preserving…

Consider a compact connected Lie group $G$ and the corresponding Lie algebra $\cal L$. Let $\{X_1,...,X_m\}$ be a set of generators for the Lie algebra $\cal L$. We prove that $G$ is uniformly finitely generated by $\{X_1,...,X_m\}$. This…

It has long been recognized as a difficult problem to determine whether the observed statistical correlation between two classical variables arise from causality or from common causes. Recent research has shown that in quantum theoretical…

The idea of this paper is to explore the existence of canonical countably saturated models for different classes of structures. It is well-known that, under CH, there exists a unique countably saturated linear order of cardinality…

We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad…

A scheme for an algebraic quantization of the causal sets of Sorkin et al. is presented. The suggested scenario is along the lines of a similar algebraization and quantum interpretation of finitary topological spaces due to Zapatrin and…

A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…

In this dissertation we develop a new formal graphical framework for causal reasoning. Starting with a review of monoidal categories and their associated graphical languages, we then revisit probability theory from a categorical perspective…

We propose an approach to quantum theory based on the energetic causal sets, introduced in Cort\^{e}s and Smolin (2013). Fundamental processes are causal sets whose events carry momentum and energy, which are transmitted along causal links…

P. Hall constructed a universal countable locally finite group U, determined up to isomorphism by two properties: every finite group C is a subgroup of U, and every embedding of C into U is conjugate in U. Every countable locally finite…

A precise definition of a black hole has long been absent in causal set theory. I first show that the local finiteness of the theory cannot be interpreted as a complete discretization condition, and the theory still admits continua, which I…