Related papers: Singularities and diffeomorphisms
As in the case of the other gauge field theories, there is so called ``gauge'' also in general relativity. This ``gauge'' is unphysical degree of freedom. There are two kinds of ``gauges'' in general relativity. These are called the first-…
Building on author's previous results in singular semi-Riemannian geometry and singular general relativity, the behavior of gauge theory at singularities is analyzed. The usual formulations of the field equations at singularities are…
A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to…
We discuss global gauge fixing on the lattice, specifically to the lattice Landau gauge, with the goal of understanding the question of why the process becomes extremely slow for large lattices. We construct an artificial "gauge-fixing"…
In an earlier paper we provided an alternative to the standard gauge concept for deriving the classical electromagnetic wave equations. This alternative involves recognition of two previously overlooked basic equations and represents a…
Diverse planning is the problem of finding multiple plans for a given problem specification, which is at the core of many real-world applications. For example, diverse planning is a critical piece for the efficiency of plan recognition…
The gauge symmetry is one of the most important concepts in modern physics, but there are two conflicting views on its meaning or interpretation. The standard view is that local gauge symmetry is the basis of the pursue of fundamental…
Let (N,g) be a nilpotent Lie group endowed with an invariant geometric structure (cf. symplectic, complex, hypercomplex or any of their `almost' versions). We define a left invariant Riemannian metric on N compatible with g to be minimal,…
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…
We try to convince the reader that the categorical version of differential geometry, called Synthetic Differential Geometry (SDG), offers valuable tools which can be applied to work with some unsolved problems of general relativity. We do…
Let N be a nilpotent Lie group and let S be an invariant geometric structure on N (cf. symplectic, complex or hypercomplex). We define a left invariant Riemannian metric on N compatible with S to be "minimal", if it minimizes the norm of…
In general relativity, the strong equivalence principle is underpinned by a geometrical interpretation of fields on spacetime: all fields and bodies probe the same geometry. This geometric interpretation implies that the parallel transport…
In the shape analysis approach to computer vision problems, one treats shapes as points in an infinite-dimensional Riemannian manifold, thereby facilitating algorithms for statistical calculations such as geodesic distance between shapes…
Via partial resolution of Abelian orbifolds we present an algorithm for extracting a consistent set of gauge theory data for an arbitrary toric variety whose singularity a D-brane probes. As illustrative examples, we tabulate the matter…
This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the…
When dealing with a spacetime, one usually searches for singularities, black holes, white holes and wormholes due to their importance to the motion of particles. There is a family of solution of the Brans-Dicke vacuum equations that has not…
In this paper we give an explicit representation of the solutions of a characteristic Cauchy problem for a class of PDEs with singular coefficients. We give the explicit solutions in terms of the Gauss hypergeometric functions, which enable…
Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…
Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of…
We study gauge properties of the general teleparallel theory of gravity, defined in the framework of Poincare gauge theory. It is found that the general theory is characterized by two kinds of gauge symmetries: a specific gauge symmetry…