Related papers: Geometric Algebra Techniques for General Relativit…
We have developed a general geometric treatment of the GCE valid for any stationary axisymmetric metric. The method is based on the remark that the world lines of objects rotating along spacely circular trajectories are in any case, for…
We retrace Davenport's solution to Wahba's classic problem of aligning two pointclouds using the formalism of Geometric Algebra (GA). GA proves to be a natural backdrop for this problem involving three-dimensional rotations due to the…
Deformed $\mathfrak{g}_2$ exceptional applications are introduced via the Clifford algebra-parametrized formalism. Using the products between multivectors of $\cl_{0,7}$, the Clifford algebra over the metric vector space $\RR^{0,7}$, and…
We define a generalized form of $L_\infty$-algebras called $E_2L_\infty$-algebras. As we show, these provide the natural algebraic framework for generalized geometry and the symmetries of double field theory as well as the gauge algebras…
Recently, an extension of teleparallelism to a Weyl geometry which allows us to easily establish conformal invariance and "geometrize" electromagnetism has been presented. In this paper, I extend a result which concerns the existence of the…
It is proved that for a vector space W, any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of [DL2] with W as a natural module. This result generalizes a result…
The aim of this work is to investigate the structure of some skew twisted algebras, when the coefficient ring is a localization of the polynomial ring over the field of characteristic zero, and an involution is provided. A parallel…
A universal symmetry algebra organizing the gravitational phase space has been recently found. It corresponds to the subset of diffeomorphisms that become physical at corners -- codimension-$2$ surfaces supporting Noether charges. It…
On the base of the distinction between covariant and contravariant metric tensor components, an approach from algebraic geometry will be proposed, aimed at finding new solutions of the Einstein's equations both in GTCCCM and in standard…
We present a novel derivation of the elastic theory of shells. We use the language of Geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools…
We show that main results of rational trigonometry (as developed by NJ Wildberger, "Divine Proportions", 2005) can be succinctly expressed using projective geometric algebra (PGA). In fact, the PGA representation exhibits distinct…
In the context of an extended General Relativity theory with boundary terms included, we introduce a new nonlinear quantum algebra involving a quantum differential operator, with the aim to calculate quantum geometric alterations when a…
Some connections between quadratic forms over the field of two elements, Clifford algebras of quadratic forms over the real numbers, real graded division algebras, and twisted group algebras will be highlighted. This allows to revisit real…
An expository approach is given on the relationship between algebraic and geometric approaches to properties of isometries in the plane and the 2-sphere.
I state and prove, in the context of a space having only the metrical and affine structure imposed by the geometrized version of Newtonian gravitational theory, a theorem analagous to that of Weyl's for a Lorentz manifold. The theorem says…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
We formulate scalar field theories coupled non-conformally to gravity in a manifestly frame-independent fashion. Physical quantities such as the $S$ matrix should be invariant under field redefinitions, and hence can be represented by the…
We perform an Hamiltonian reduction on a classical \cw(\cg, \ch) algebra, and prove that we get another \cw(\cg, \ch$'$) algebra, with $\ch\subset\ch'$. In the case $\cg=S\ell(n)$, the existence of a suitable gauge, called Generalized…
Geometric vertex algebras are a simplified version of Huang's geometric vertex operator algebras. We give a self-contained account of the equivalence of geometric vertex algebras with Z-graded vertex algebras.
In four space-time dimensions, there are good theoretical reasons for believing that General Relativity is the correct geometrical theory of gravity, at least at the classical level. If one admits the possibility of extra space-time…