Related papers: Vector- and tensor-valued descriptors for spatial …
The de Sitter manifold admits a wide variety of interesting coordinatizations. The 'atlas' is a compilation of the coordinate charts referenced throughout the literature, and is presented in the form of tables, the starting point being the…
We consider the dynamics of tensor and scalar gravitational fields in the Relativistic Theory of Gravitation with the Minkowskian vacuum metric and generalize the formulation to the massless graviton. The potential of scalar field is…
We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors. We demonstrate the effectiveness of the approach by proving of a number of integral identities with vector integrands.
We define two notions of discrete dimension based on the Minkowski and Hausdorff dimensions in the continuous setting. After proving some basic results illustrating these definitions, we apply this machinery to the study of connections…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
The metric-affine gravity provides a useful framework for analyzing gravitational dynamics since it treats metric tensor and affine connection as fundamentally independent variables. In this work, we show that, a metric-affine gravity…
Tensor models are measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as additionally to the…
In this paper I shall consider various possible scalar-vector-tensor field theories which might be used to describe the Universe. After imposing numerous constraints of a physical and mathematical nature on the theories under consideration,…
An algorithm is given for computing explicit formulas for the generators of relations among the invariant rational functions for vector-valued bilinear forms. These formulas have applications in the geometry of Riemannian submanifolds and…
A classification of SL$(n)$ contravariant Minkowski valuations on convex functions and a characterization of the projection body operator are established. The associated LYZ measure is characterized. In addition, a new SL$(n)$ covariant…
The second-order formula of Minkowski functionals in weakly non-Gaussian fields is compared with the numerical $N$-body simulations. Recently, weakly non-Gaussian formula of Minkowski functionals is extended to include the second-order…
Pairs of metrics in a two-dimensional linear vector space are considered, one of which is a Minkowski type metric. Their simultaneous diagonalizability is studied and canonical presentations for them are suggested.
Future observations of the large-scale structure have the potential to investigate cosmological models with a high degree of complexity, including the properties of gravity on large scales, the presence of a complicated dark energy…
Tensor networks give simple representations of complex quantum states. They have proven useful in the study of condensed matter systems and conformal fields, and recently have provided toy models of AdS/CFT. Underlying the tensor network -…
Tensor Minkowski Functionals (TMFs) are tensorial generalizations of the usual Minkowski Functionals which are scalar quantities. We introduce them here for use in cosmological analysis, in particular to analyze CMB maps. They encapsulate…
Using general but simple covariance arguments, we classify the `quantum' Minkowski spaces for dimensionless deformation parameters. This requires a previous analysis of the associated Lorentz groups, which reproduces a previous…
A general framework for effective theories propagating two tensor and one scalar degrees of freedom is investigated. Geometrically, it describes dynamical foliation of spacelike hypersurfaces coupled to a general background, in which the…
Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for…
We give a systematic and thorough study of geometric notions and results connected to Minkowski's measure of symmetry and the extension of the well-known Minkowski functional to arbitrary, not necessarily symmetric convex bodies K on any…
The classification of continuous, translation invariant Minkowski valuations which are contravariant (or covariant) with respect to the complex special linear group is established in a 2-dimensional complex vector space. Every such…