Related papers: Computer algebra in gravity
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
For the quadratic Poincar\'e gauge theory of gravity (PG) we consider the FLRW cosmologies using an isotropic Bianchi representation. Here the considered cosmologies are for the general case: all the even and odd parity terms of the…
The first aim of this paper is to show that any finite-dimensional reductive Lie algebra and its finite-dimensional completely reducible representation can be embedded into some PC Lie algebra. The second aim is to find the structure of a…
We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by…
We investigate the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science. First, using the multiparticle spacetime algebra (MSTA, the geometric algebra of a relativistic…
Determining visibility in planar polygons and arrangements is an important subroutine for many algorithms in computational geometry. In this paper, we report on new implementations, and corresponding experimental evaluations, for two…
The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows to test loop quantum gravity in a large class of minisuperspaces and to investigate its features…
We introduce the C++ library Wedge, based on GiNaC, for symbolic computations in differential geometry. We show how Wedge makes it possible to use the language C++ to perform such computations, and illustrate some advantages of this…
These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts. In particular, this includes a discussion of simplification…
We investigate extensions of Malcev algebras and give an explicit example of extended algebras. We present a new algebraic identity, which can be regarded as a generalization of the Jacobi identity or the Malcev identity. As applications to…
We review Extended Theories of Gravity in metric and Palatini formalism pointing out their cosmological and astrophysical application. The aim is to propose an alternative approach to solve the puzzles connected to dark components.
Numerical Relativity is a mature field with many applications in Astrophysics, Cosmology and even in Fundamental Physics. As such, we are entering a stage in which new sophisticated methods adapted to open problems are being developed. In…
Many fundamental questions in theoretical computer science are naturally expressed as special cases of the following problem: Let $G$ be a complex reductive group, let $V$ be a $G$-module, and let $v,w$ be elements of $V$. Determine if $w$…
This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the determinant being constructed as it should, as a signed…
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry,…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
This essay aims at emphasizing the potential of a synergy between quantum gravity and the quantum computing technologies. Such a combination would be beneficial for both understanding the Planck scale physics and the stimulation of…
Maxwell extension of affine algebra with additional tensorial generators is given. Using the methods of nonlinear realizations, we found the transformation rules for group parameters and corresponding generators. Gauging the Maxwell-affine…
The quantum-reduced loop-gravity technique has been introduced for dealing with cosmological models. We show that it can be applied rather generically: anytime the spatial metric can be gauge-fixed to a diagonal form. The technique selects…
Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is required to create a user extension for an existing computer…