Related papers: Symbolic and Numerical Analysis in General Relativ…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
The goal of this paper is to give a representation-theoretic interpretation of the sine-Gordon equation. We consider a vertex operator representation of affine Kac-Moody algebra \hat{sl_2} on the space of differential operators. In this…
By using the Gitman-Lyakhovich-Tyutin canonical analysis for higher-order theories a four-dimensional Chern-Simons modification of general relativity is analyzed. The counting of physical degrees of freedom, the symmetries, and the…
It has recently been shown that generalized connections of the (A)dS space symmetry algebra provide an effective geometric and algebraic framework for all types of gauge fields in (A)dS, both for massless and partially-massless. The…
Due to the occurrence of large exceptional Lie groups in supergravity, calculations involving explicit Lie algebra and Lie group element manipulations easily become very complicated and hence also error-prone if done by hand. Research on…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…
Hamilton-Jacobi theory for general relativity provides an elegant covariant formulation of the gravitational field. A general `coordinate-free' method of integrating the functional Hamilton-Jacobi equation for gravity and matter is…
The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively…
We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
A frame approach to determining the most general solution admitting a desired symmetry group has been examined previously in Riemannian and teleparallel geometries with some success. In teleparallel geometries, one must determine the…
We present numerical solutions of several spacetimes of physical interest, including binary black hole mergers, in shift-symmetric Einstein-scalar-Gauss-Bonnet (ESGB) gravity, and describe our methods for solving the full equations of…
We study measures, finitely additive measures, regular measures, and $\sigma$-additive measures that can attain even infinite values on the quantum logic of a Hilbert space. We show when particular classes of non-negative measures can be…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
We consider a simpler geometrical formulation of General Relativity based on non-metricity, known as Coincident General Relativity. We study the ADM formulation of the theory and perform a detailed Hamiltonian analysis. We explicitly show…
For some research questions that involve Spin(p, q) representation theory, using symbolic algebra based techniques might be an attractive option for simplifying and manipulating expressions. Yet, for some such problems, especially as they…
Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's…
Cadabra is a new computer algebra system designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification taking care of Bianchi and Schouten identities, for…
The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…
Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional…