Related papers: Addendum: Observables for General Relativity relat…
We report about significant enhancements of the complex algebraic geometry theorem proving subsystem in GeoGebra for automated proofs in Euclidean geometry, concerning the extension of numerous GeoGebra tools with proof capabilities. As a…
The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables…
In the last few decades, extensions of General Relativity have reached always more attention especially in view of possible breakdowns of the standard $\Lambda$CDM paradigm at intermediate and high redshift regimes. If General Relativity…
In this paper, we generalize some of the results of [9], and add some new results. Furthermore, we take a closer look at strongly simple algebras, which are introduced in [9].
The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role…
Known or essentially known results about duals of interpolation spaces are presented, taking a point of view sometimes slightly different from the usual one. Particular emphasis is placed on Alberto Calderon's theorem describing the duals…
In this letter a new formula for light deflection is derived using only physically observable concepts. The general result is specialized to cosmological perturbation theory and expressed in terms of gauge--invariant perturbation variables.…
A corrigendum of a former result on semisimplicity of the category of integrable modules of a q-boson algebra is given with a counter example.
We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one…
We consider the impact of some known extensions of General Relativity in observables that will be available with the Galileo positioning systems, and draw conclusions as to the possibility of measuring them. We specifically address the…
The laws of geometric optics and their corrections are derived for scalar, electromagnetic, and gravitational waves propagating in generic curved spacetimes. Local peeling-type results are obtained, where different components of…
For two semi-simple algebras $A$ and $B$ over an arbitrary ground field $F$, we give a numerical criterion when $\Hom_F(A,B)$, the set of $F$-algebra homomorphisms between them, is non-empty. We also determine when the orbit set $B^\times…
The Teleparallel Theory is equivalent to General Relativity, but whereas in the latter gravity has to do with curvature, in the former gravity is described by torsion. As is well known, there is in the literature a host of alternative…
Let us consider a Lie (super)algebra $G$ spanned by $T_{\alpha}$ where $T_{\alpha}$ are quantum observables in BV-formalism. It is proved that for every tensor $c^{\alpha_1...\alpha_k}$ that determines a homology class of the Lie algebra…
In the theory of General Relativity, gravity is described by a metric which couples minimally to the fields representing matter. We consider here its "veiled" versions where the metric is conformally related to the original one and hence is…
As shown by Ashtekar in the mid 80's, general relativity can be extended to incorporate degenerate metrics. This extension is not unique, however, as one can change the form of the hamiltonian constraints and obtain an {\it alternative}…
In this lecture I build up the motivation for relativity and gravitation based on general principles and common sense considerations which should fall in the sphere of appreciation of a general reader. There is a novel way of looking at…
In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than…
We consider simple modules over the McConnell--Pettit algebras. We show that both induction and contraction yield simple modules for the extremes of the global dimension.
We investigate a simple generalization of the metric exponential $f(R)$ gravity theory that is cosmologically viable and compatible with solar system tests of gravity. We show that, as compared to other viable $f(R)$ theories, its steep…