Related papers: The Extending for Composite Skyrme Model
We extend in several directions invariant theory results of Chevalley, Shephard and Todd, Mitchell and Springer. Their results compare the group algebra for a finite reflection group with its coinvariant algebra, and compare a group…
We provide, through the framework of extended geometry, a geometrisation of the duality symmetries appearing in magical supergravities. A new ingredient is the general formulation of extended geometry with structure group of non-split real…
Cosmological observations are beginning to reach a level of precision that allow us to test some of the most fundamental assumptions in our working model of the Universe. One such an assumption is that gravity is governed by the General…
We consider the Chiral Cosmological Models (CCMs) and modified gravity theories associated with them. Generalization of the superpotential method for a general CCM with several scalar fields is performed, and the method of construction CCMs…
With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we find some new $q$-supercongruences.…
We review the group-geometric approach to supergravity theories, in the perspective of recent developments and applications. Usual diffeomorphisms, gauge symmetries and supersymmetries are unified as superdiffeomorphisms in a supergroup…
This note provides an overview of the notion of observable within the setting of multisymplectic geometry. We essentially follow the ideas described by F. H\'elein and J. Kouneiher [17] [18] [19] and in particular in keeping with the…
In this review paper we present some basic notions about f(R) theories of gravity and some simple cosmological models derived from it. We first make an introduction to General Relativity (GR), followed by the discussion of…
In this lecture note, we give a basic introduction to the rapidly developing concepts of generalized symmetries, from the perspectives of both high energy physics and condensed matter physics. In particular, we emphasize on the (invertible)…
We give the full representation theory of the gravitational extended corner symmetry group in two-dimensions. This includes projective representations, which correspond to representations of the quantum corner symmetry group. We find that…
We introduce a hierarchical system of approximations for summing both conventional perturbation theory and large N vector expansions of models in quantum field theory and condensed matter physics. Each stage of the hierarchy consists of a…
In this article, we go on to discuss about a series of infinite dimensional extension of the theorems in [3], [5], [6]. We also prove a similar Geraghty type constructions for Fisher ([5]) in infinite dimension, using similar techniques as…
We generalize the virial theorem in f(R) modified gravity using the collisionless Boltzmann equation. We find supplementary geometric terms in the modified Einstein equation providing an effective contribution to the gravitational energy.…
This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.
We present a simple unifying gauge theoretical formulation of gravitational theories in two dimensional spacetime. This formulation includes the effects of a novel matter-gravity coupling which leads to an extended de Sitter symmetry…
Modified theories of gravity have been invoked recently as an alternative to dark energy, in an attempt to explain the apparent accelerated expansion of the universe at the present time. In order to describe inhomogeneities in cosmological…
We study in some detail the "extended Kerr-Schild" formulation of general relativity, which decomposes the gauge-independent degrees of freedom of a generic metric into two arbitrary functions and the choice of a flat background tetrad. We…
Linear superposition of gravitational fields is shown to be possible for a large class of spacetimes, in some specific coordinates. Explicit examples are presented.
In a recent paper (Appl. Math. Comput. 215, 1622--1645, 2009), the authors proposed a method of summation of some slowly convergent series. The purpose of this note is to give more theoretical analysis for this transformation, including the…
A survey is made of some recent ideas and progress in the phenomenological applications of Supersymmetry (SUSY). We describe the success of SUSY-GUT models, the expected experimental signatures and present limits on SUSY partner particles,…