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A frame approach to determining the most general solution admitting a desired symmetry group has been examined previously in Riemannian and teleparallel geometries with some success. In teleparallel geometries, one must determine the…
We develop a comprehensive geometric framework for defining spaces $\mathcal{G}(M,E)$ of nonlinear generalized sections of vector bundles $E \to M$ containing spaces of distributional sections $\mathcal{D}'(M, E)$. Our theory incorporates…
We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is…
Based on a study of recently proposed solution of 2 dim. black hole we argue that the space-time singularities of general relativity may be described by topological field theories (TFTs). We also argue that in general TFT is a field theory…
As an extension of the Robinson-Trautman solutions of D=4 general relativity, we investigate higher dimensional spacetimes which admit a hypersurface orthogonal, non-shearing and expanding geodesic null congruence. Einstein's field…
We show that the Schwarzschild solution can be embedded in a class of nonstandard solutions of the vacuum Einstein's equations with arbitrary rotation curves. These nonstandard solutions have to be taken as physical if dark matter as needed…
The Doplicher, Fredenhagen and Roberts (DFR) noncommutative (NC) formalism is propose in a curved space-time. In DFR approach, the NC parameter is promoted to the set of coordinates of the space-time. As consequence, the field theory…
The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at…
It is shown that the geometry of parallelizable manifolds can be extended to non-parallelizable ones by extending the connection that a global frame field would define on a parallelizable manifold to a connection that a singular frame field…
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of…
The subject of this PhD thesis is noncommutative geometry - more specifically spectral triples - and how it can be generalized to semi-Riemannian manifolds generally, and Lorentzian manifolds in particular. The first half of this thesis…
We construct matter field theories in ``theory space'' that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and…
We develop a systematic framework for studying target space duality at the classical level. We show that target space duality between manifolds M and Mtilde arises because of the existence of a very special symplectic manifold. This…
We give from first principles the non-relativistic limit of scalar and Dirac fields in curved spacetime. We aim to find general relativistic corrections to the quantum theory of particles affected by Newtonian gravity, a regime nowadays…
It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d-dimensions (one-time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained…
We consider the duality between General Relativity and the theory of Einstein algebras, in the extended setting where one permits non-Hausdorff manifolds. We show that the duality breaks down, and then go on to discuss a sense in which…
We revisit universal features of duality in linear and nonlinear relativistic scalar and Abelian 1-form theories with single or multiple fields, which exhibit ordinary or generalized global symmetries. We show that such global symmetries…
Lifshitz spacetimes are possible gravitational duals to strongly coupled field theories with an anisotropic scaling symmetry. These spacetimes however, have a null curvature singularity. We find that higher dimensional embeddings of…
We study general properties of the classical solutions in non-polynomial closed string field theory and their relationship with two dimensional conformal field theories. In particular we discuss how different conformal field theories which…
Toroidal backgrounds for bosonic strings are used to understand target space duality as a symmetry of string field theory and to study explicitly issues in background independence. Our starting point is the notion that the string field…