Related papers: Forces on an exterior algebra bundle

The author investigates the general Lie algebra of operators of coordinates, momenta, and Lorentz group generators, which can be used in quantum gravity, theories with generalized uncertainty principle, double and triple relativity and…

On the bundles of WZW chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement the action of outer automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms respect the…

We briefly discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to…

We establish results about algebraic shifting of simplicial complexes and use them to compare different shifting operations. In particular, we show that each shifting operation does not decrease the number of facets, and that the exterior…

In the light of intriguing results of C.C.Barros, we investigate in this thesis the possibilities of geometrical interpretation of all the fundamental interactions in order to unify them. More exactly we try to supply a unified geometrical…

With the help of Weil polynomials on the Lie algebra of the Poincar\'e group in D dimensions, we construct a Lagrangian form for higher dimensional gravity on a principal fibre bundle whose base space is an even-dimensional Riemann-Cartan…

This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to: i) achieve a clear understanding of how different…

The boundary conditions of a non-trivial string background are classified. To this end we need traces on various spaces of conformal blocks, for which generalizations of the Verlinde formula are presented.

After casting Euler-$\alpha$ equations into vorticity-stream function formula, we obtain some very useful estimates from the properties of the vorticity formula in exterior domain. Basing on these estimates, one can have got the global…

In this article we provide a more detailed account of the geometry and topology of the composite bundle formalism introduced by Tresguerres in Phys. Rev. D 66 (2002) 064025 [1] to accommodate gravitation as a gauge theory. In the first half…

The effect of edges and apertures on the Casimir energy of an arrangement of plates and boundaries can be calculated in terms of an effective nonlocal lower-dimensional field theory that lives on the boundary. This formalism has been…

The local Lorentz group is introduced in flat space-time, where the resulting Dirac and Yang-Mills equations are found, and then generalized to curved space-time: if matter is neglected, the Lorentz connection is identified with the…

We consider geometric variational problems for a functional defined on a curve in three-dimensional space. The functional is assumed to be written in a form invariant under the group of Euclidean motions. We present the Euler-Lagrange…

The most general geometrical scenario in which the brane-world program can be implemented is investigated. The basic requirement is that it should be consistent with the confinement of gauge interaction, the existence of quantum states and…

An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…

Within the framework of geodetic brane gravity, the Universe is described as a 4-dimensional extended object evolving geodetically in a higher dimensional flat background. In this paper, by introducing a new pair of canonical fields…

It is well known that in four or more dimensions, there exist exotic manifolds; manifolds that are homeomorphic but not diffeomorphic to each other. More precisely, exotic manifolds are the same topological manifold but have inequivalent…

We give a global formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields for the generalized situation when the "duality structure" of the Abelian gauge theory is described by a flat symplectic vector…

In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This…

Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a…