Related papers: DGLA Actions: An Application in GR
In this paper, first using the higher derived brackets, we give the controlling algebra of relative difference Lie algebras, which are also called crossed homomorphisms or differential Lie algebras of weight 1 when the action is the adjoint…
We obtain a new form for the action of a nonrelativistic particle coupled to Newtonian gravity. The result is different from that existing in the literature which, as shown here, is riddled with problems and inconsistencies. The present…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
We extend the f(R) gravity action by including a generic dependence upon the Weyl tensor, and further generalize it to supergravity by using the super-curvature (R) and super-Weyl (W) chiral superfields in N=1 chiral curved superspace. We…
Motivated by quantum mechanical considerations we earlier suggested an alternative action for discretised quantum gravity which has a dimension of length. It is the so called "linear" action. The proposed action is a "square root" of the…
Complete sets of bases of differential invariants, operators of invariant differentiation and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of…
We construct the deformation functor associated with a pair of morphisms of differential graded Lie algebras, and use it to study infinitesimal deformations of holomorphic maps of compact complex manifolds. In particular, using L-infinity…
We generalize the notion of kinematical Lie algebra introduced in physics for the classification of the various possible relativity algebras an isotropic spacetime can accommodate. We first give an elementary proof of the fact that such a…
The gauge theoretical formulation of general relativity is presented. We are only concerned with local intrinsic geometry, i.e. our space-time is an open subset of a four-dimensional real vector space. Then the gauge group is the set of…
To unify general relativity and quantum theory is hard in part because they are formulated in two very different mathematical languages, differential geometry and functional analysis. A natural candidate for bridging this language gap, at…
We study realizations of Lie algebras by vector fields. A correspondence between classification of transitive local realizations and classification of subalgebras is generalized to the case of regular local realizations. A reasonable…
We present some recently discovered infinite dimensional Lie algebras that can be understood as extensions of the algebra Map(M,g) of maps from a compact p-dimensional manifold to some finite dimensional Lie algebra g. In the first part of…
We construct invariant differential operators acting on sections of vector bundles of densities over a smooth manifold without using a Riemannian metric. The spectral invariants of such operators are invariant under both the diffeomorphisms…
This paper reframes Riemannian geometry as a generalized Lie algebra allowing the equations of both RG and then General Relativity to be expressed as commutation relations among fundamental operators. We begin with an Abelian Lie algebra of…
The goal of this paper is to propose and discuss a practical way to implement the Dirac algorithm for constrained field models defined on spatial regions with boundaries. Our method is inspired in the geometric viewpoint developed by Gotay,…
We extend the concept of a partial group action to non-associative algebras in a variety \(\mathcal{V}(I)\), solve the globalization problem within \(\mathcal{V}(I)\) and examine its universal property. It is achieved using what we call the…
Gauged supergravity (SG) with single scalar (dilaton) and arbitrary scalar potential is considered. Such dilatonic gravity describes special RG flows in extended SG where scalars lie in one-dimensional submanifold of total space. The…