相关论文: Mining metrics for buried treasure

We suggest two metrics for assessing the quality of atomistic configurations of disordered materials, both of which are based on quantifying the orientational distribution of neighbours around each atom in the configuration. The first…

A recently developed tool allows for a description of spacetime as a manifold with a Lorentz-invariant (lower) limit length built-in. This is accomplished in terms of geometric quantities depending on two spacetime events (bitensors) and…

Jarnik's identity plays a major role in classical simultaneous approximation to two real numbers. O. German [2] has shown a generalization to the weighted setting in which the identity has to be replaced by two inequalities. His methods…

A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…

Diversities are an extension of the concept of a metric space which assign a non-negative value to every finite set of points, rather than just pairs. A general theory of diversities has been developed which exhibits many deep analogies to…

Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a…

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…

Given a flat metric one may generate a local Hamiltonian structure via the fundamental result of Dubrovin and Novikov. More generally, a flat pencil of metrics will generate a local bi-Hamiltonian structure, and with additional…

Inspired by some recent works of Tippett-Tsang and Mallary-Khanna-Price, we present a new spacetime model containing closed timelike curves (CTCs). This model is obtained postulating an ad hoc Lorentzian metric on $\mathbb{R}^4$, which…

The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals…

We compare metrics obtained through analytic perturbation theory with their numerical counterparts. The analytic solutions are computed with the CMMR post-Minkowskian and slow rotation approximation due to Cabezas et al. (2007) for an…

The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…

Galatius and Randal-Williams defined a topology on the set of closed submanifolds of ${\mathbb R}^n$. B\"okstedt and Madsen proved that a $C^1$-version of this topology is metrizable by showing that it is regular and second countable. Using…

We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor…

We derive curvature counterterms in two-dimensional gravity coupled to conformal matter up to infinite order. By construction the higher-order action is equivalent to a finite first-order theory with auxiliary scalar. Due to this…

The mathematical foundations of relativistic quantum mechanics is largely based upon the discovery of the Pauli and Dirac matrices. An algebra which lies at an even more fundamental level is the geometric Clifford algebra with metric…

This is a write-up of a talk given at the CATMI meeting in Bergen in July 2023, and is an introduction to a category-theoretic perspective on metric spaces. A metric space is a set of points such that between each pair of points there is a…

A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a…

It is well known that in general relativity theory two spacetimes whose metrics are related by a coordinate transformation are physically equivalent. However, given two line elements, it is virtually impossible to implement the most general…

The conformal properties of metrics are meaningful in Riemannian and Finsler geometry, and cubic metrics are useful in physics and biology. In this paper, we study the conformally flat cubic metrics with weakly isotropic scalar curvature.…