Related papers: Computer algebra in gravity: Programs for (non-)Ri…
Gravitational lenses are presently playing an important role in astrophysics. By means of these lenses the parameters of the deflector such as its mass, ellipticity, etc. and Hubble's constant can be determined. Using C, Xforms, Mesa and…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
We examine the relative performance of algorithms for the calculation of curvature in spacetime. The classical coordinate component method is compared to two distinct versions of the Newman-Penrose tetrad approach for a variety of…
After summarizing basic concepts for the exterior algebra we firstly discuss the gauge structure of the bundle over base manifold for deciding the form of the gravitational sector of the total Lagrangian in any dimensions. Then we couple…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
In this work we provide the motivation for considering non-Riemannian models in cosmology. Non-Riemannian extensions of general relativity theory have been studied for a long time. In such theories the spacetime continuum is no longer…
The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main…
In this article we give the realization of the Klein's Program for geometrical structures (Riemannian spaces and fiber bundles with connection) with arbitrary variable curvature within the framework of infinite deformed groups. These groups…
This Thesis is devoted to the study of Metric-Affine Theories of Gravity and Applications to Cosmology. The thesis is organized as follows. In the first Chapter we define the various geometrical quantities that characterize a non-Riemannian…
In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
The variational field equations of Brans-Dicke scalar-tensor theory of gravitation are given in a non-Riemannian setting in the language of exterior differential forms over 4-dimensional spacetimes. A conformally re-scaled Robinson-Trautman…
This is the second in a series of two articles introducing the Gravitas computational general relativity framework, in which we now focus upon the design and capabilities of Gravitas's numerical subsystem, including its ability to perform…
In this paper we present our recent work in developing a computer-algebra tool for systems of partial differential equations (PDEs), termed "Kranc". Our work is motivated by the problem of finding solutions of the Einstein equations through…
A new simplified approach for teaching electromagnetism is presented using the formalism of geometric algebra (GA) which does not require vector calculus or tensor index notation, thus producing a much more accessible presentation for…
Differential forms is a highly geometric formalism for physics used from field theories to General Relativity (GR) which has been a great upgrade over vector calculus with the advantages of being coordinate-free and carrying a high degree…
Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern--Simons models consisting of fractional-spin fields coupled to higher-spin gravity and internal non-abelian gauge fields. The gauge algebras consist of Lorentz-tensorial…