Related papers: Scale transformations in metric-affine geometry
We study the classification of ultrametric spaces based on their small scale geometry (uniform homeomorphism), large scale geometry (coarse equivalence) and both (all scale uniform equivalences). We prove that these equivalences can be…
The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…
We undertake the construction of quadratic parity-violating terms involving the curvature in the four-dimensional metric-affine gravity. We demonstrate that there are only 12 linearly independent scalars, plus an additional one that can be…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
While not generally a conservation law, any symmetry of the equations of motion implies a useful reduction of any second-order equationto a first-order equation between invariants, whose solutions (first integrals) can then be integrated by…
The reconstruction of fundamental parameters in supersymmetric theories requires the evolution to high scales, where the characteristic regularities in mechanisms of supersymmetry breaking become manifest. We have studied a set of…
Many systems of both theoretical and applied interest display multi-affine scaling at small length scales. We demonstrate analytically and numerically that when vertical discontinuities are introduced into a self-affine surface, the surface…
This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space,…
A general scheme of constructing scalar-tensor equivalents to modified gravitational actions are studied using the algebra of exterior differential forms and the first order formalism that allows an independent connection and coframe. By…
A recent paper showed how to find sets of finite affine or projective planes constructed on a common set of points, so that lines of one plane meet lines of a different plane in at most two points. In this paper, those results are…
We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic…
In this paper, the association scheme defined on the flags of a finite generalized quadrangle is considered. All possible fusions of this scheme are listed, and a full description for those of classes 2 and 3 is given. Furthermore, it is…
Area metrics are an intriguing generalization of length metrics which appears in several quantum-gravity approaches. We describe the space of diffeomorphism-invariant area-metric actions quadratic in fluctuations and derivatives. A general…
Meta-conformal transformations are constructed as dynamical symmetries of the linear transport equation in $d$ spatial dimensions. In one and two dimensions, the associated Lie algebras are infinite-dimensional and isomorphic to the direct…
Metric approximate categories, or metagories, for short, are metrically enriched graphs. Their structure assigns to every directed triangle in the graph a value which may be interpreted as the area of the triangle; alternatively, as the…
In metric-affine geometry, autoparallels are generically non-variational, i.e., they are not the extremals of any action integral. The existence of a parametrization-invariant action principle for autoparallels is a long-standing open…
Distance transformation is an image processing technique used for many different applications. Related to a binary image, the general idea is to determine the distance of all background points to the nearest object point (or vice versa). In…
Conformal symmetries appear in many parts of physics and play a unique role in exploring the Universe. In this work, we consider the possibility of constructing conformal theories of gravity in the Symmetric Teleparallel Gravity framework,…
Commensurate scale relations relate observables to observables and thus are independent of theoretical conventions, such as the choice of intermediate renormalization scheme. The physical quantities are related at commensurate scales which…
In this second part of the paper, dedicated to theories with extra dimensions, a new physical notion about the "tensor length scale" is introduced, based on the gravitational theories with covariant and contravariant metric tensor…