Related papers: Distance Domains: Completeness
A generalized scalar-tensor theory is investigated whose cosmological term depends on both a scalar field and its time derivative. A correspondence with solutions of five-dimensional Space-Time-Matter theory is noted. Analytic solutions are…
The standard definition of cylindrical symmetry in General Relativity is reviewed. Taking the view that axial symmetry is an essential pre-requisite for cylindrical symmetry, it is argued that the requirement of orthogonal transitivity of…
Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They…
The concept of synthetic dimensions has emerged as a powerful framework in photonics and atomic physics, enabling the exploration of high-dimensional physics beyond conventional spatial constraints. Originally developed for quantum…
Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional…
The distance conjecture states that for theories with moduli coupled to gravity a tower of states becomes light exponentially in the geodesic distance in moduli space. This specifies how effective field theories break down for large field…
The regularity of monotone transport maps plays an important role in several applications to PDE and geometry. Unfortunately, the classical statements on this subject are restricted to the case when the measures are compactly supported. In…
We survey a new area of parameter-free similarity distance measures useful in data-mining, pattern recognition, learning and automatic semantics extraction. Given a family of distances on a set of objects, a distance is universal up to a…
The article is devoted to approximate, global and along curves differentiability of functions over non-archimedean infinite fields with non-trivial valuations. Fields with zero and non-zero characteristics are considered. Spaces of…
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
This is a general introduction to duality in field theories. The existence and breaking of global symmetries is used as a guideline to systematically prove duality between different field theories. Systems discussed include abelian and…
We discuss the cosmology of axion-scalar systems in asymptotic limits of type IIB/F-theory flux compactifications. These results allow us to test a putative extension of the Distance Conjecture in a dynamical setting, which posits that…
The behaviour of statistical relational representations across differently sized domains has become a focal area of research from both a modelling and a complexity viewpoint.Recently, projectivity of a family of distributions emerged as a…
We identify boundary terms renormalizing the free on-shell actions for massless fields of arbitrary spin, including electromagnetism and linearized gravity, with boundary conditions allowing for supertranslation-like asymptotic symmetries.…
A new characterization of convexity of a planar domain is obtained. Its derivation involves two classical facts: the Varadhan's formula, expressing the distance function with respect to the domain's boundary via real-valued solutions of the…
The theory of total positivity for reductive groups is here extended to the case of symmetric spaces.
Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of such spaces and their patch spaces, obtained by joining the original topology…
A multisymplectic setting for classical field theories subjected to non-holonomic constraints is presented. The infinite dimensional setting in the space of Cauchy data is also given.
The aim of this paper is to discus the relations between various notions of sequential completeness and the corresponding notions of completeness by nets or by filters in the setting of quasi-metric spaces. We propose a new definition of…