842 research outputs found
Dequantisation of the Dirac Monopole
Using a sheaf-theoretic extension of conventional principal bundle theory,
the Dirac monopole is formulated as a spherically symmetric model free of
singularities outside the origin such that the charge may assume arbitrary real
values. For integral charges, the construction effectively coincides with the
usual model. Spin structures and Dirac operators are also generalised by the
same technique.Comment: 22 pages. Version to appear in Proc. R. Soc. London
Profiles of inflated surfaces
We study the shape of inflated surfaces introduced in \cite{B1} and
\cite{P1}. More precisely, we analyze profiles of surfaces obtained by
inflating a convex polyhedron, or more generally an almost everywhere flat
surface, with a symmetry plane. We show that such profiles are in a
one-parameter family of curves which we describe explicitly as the solutions of
a certain differential equation.Comment: 13 pages, 2 figure
Translations and dynamics
We analyze the role played by local translational symmetry in the context of
gauge theories of fundamental interactions. Translational connections and
fields are introduced, with special attention being paid to their universal
coupling to other variables, as well as to their contributions to field
equations and to conserved quantities.Comment: 22 Revtex pages, no figures. Published version with minor correction
On globally non-trivial almost-commutative manifolds
Within the framework of Connes' noncommutative geometry, we define and study
globally non-trivial (or topologically non-trivial) almost-commutative
manifolds. In particular, we focus on those almost-commutative manifolds that
lead to a description of a (classical) gauge theory on the underlying base
manifold. Such an almost-commutative manifold is described in terms of a
'principal module', which we build from a principal fibre bundle and a finite
spectral triple. We also define the purely algebraic notion of 'gauge modules',
and show that this yields a proper subclass of the principal modules. We
describe how a principal module leads to the description of a gauge theory, and
we provide two basic yet illustrative examples.Comment: 34 pages, minor revision
A gauge theoretical view of the charge concept in Einstein gravity
We will discuss some analogies between internal gauge theories and gravity in
order to better understand the charge concept in gravity. A dimensional
analysis of gauge theories in general and a strict definition of elementary,
monopole, and topological charges are applied to electromagnetism and to
teleparallelism, a gauge theoretical formulation of Einstein gravity.
As a result we inevitably find that the gravitational coupling constant has
dimension , the mass parameter of a particle dimension ,
and the Schwarzschild mass parameter dimension l (where l means length). These
dimensions confirm the meaning of mass as elementary and as monopole charge of
the translation group, respectively. In detail, we find that the Schwarzschild
mass parameter is a quasi-electric monopole charge of the time translation
whereas the NUT parameter is a quasi-magnetic monopole charge of the time
translation as well as a topological charge. The Kerr parameter and the
electric and magnetic charges are interpreted similarly. We conclude that each
elementary charge of a Casimir operator of the gauge group is the source of a
(quasi-electric) monopole charge of the respective Killing vector.Comment: LaTeX2e, 16 pages, 1 figure; enhanced discussio
Nonsense mutations in alpha-II spectrin in three families with juvenile onset hereditary motor neuropathy
Distal hereditary motor neuropathies are a rare subgroup of inherited peripheral neuropathies hallmarked by a length-dependent axonal degeneration of lower motor neurons without significant involvement of sensory neurons. We identified patients with heterozygous nonsense mutations in the alpha II-spectrin gene, SPTAN1, in three separate dominant hereditary motor neuropathy families via next-generation sequencing. Variable penetrance was noted for these mutations in two of three families, and phenotype severity differs greatly between patients. The mutant mRNA containing nonsense mutations is broken down by nonsense-mediated decay and leads to reduced protein levels in patient cells. Previously, dominant-negative alpha II-spectrin gene mutations were described as causal in a spectrum of epilepsy phenotypes
A Categorical Equivalence between Generalized Holonomy Maps on a Connected Manifold and Principal Connections on Bundles over that Manifold
A classic result in the foundations of Yang-Mills theory, due to J. W.
Barrett ["Holonomy and Path Structures in General Relativity and Yang-Mills
Theory." Int. J. Th. Phys. 30(9), (1991)], establishes that given a
"generalized" holonomy map from the space of piece-wise smooth, closed curves
based at some point of a manifold to a Lie group, there exists a principal
bundle with that group as structure group and a principal connection on that
bundle such that the holonomy map corresponds to the holonomies of that
connection. Barrett also provided one sense in which this "recovery theorem"
yields a unique bundle, up to isomorphism. Here we show that something stronger
is true: with an appropriate definition of isomorphism between generalized
holonomy maps, there is an equivalence of categories between the category whose
objects are generalized holonomy maps on a smooth, connected manifold and whose
arrows are holonomy isomorphisms, and the category whose objects are principal
connections on principal bundles over a smooth, connected manifold. This result
clarifies, and somewhat improves upon, the sense of "unique recovery" in
Barrett's theorems; it also makes precise a sense in which there is no loss of
structure involved in moving from a principal bundle formulation of Yang-Mills
theory to a holonomy, or "loop", formulation.Comment: 20 page
The noncommutative geometry of Yang-Mills fields
We generalize to topologically non-trivial gauge configurations the
description of the Einstein-Yang-Mills system in terms of a noncommutative
manifold, as was done previously by Chamseddine and Connes. Starting with an
algebra bundle and a connection thereon, we obtain a spectral triple, a
construction that can be related to the internal Kasparov product in unbounded
KK-theory. In the case that the algebra bundle is an endomorphism bundle, we
construct a PSU(N)-principal bundle for which it is an associated bundle. The
so-called internal fluctuations of the spectral triple are parametrized by
connections on this principal bundle and the spectral action gives the
Yang-Mills action for these gauge fields, minimally coupled to gravity.
Finally, we formulate a definition for a topological spectral action.Comment: 14 page
Gravitational Waves: Just Plane Symmetry
We present some remarkable properties of the symmetry group for gravitational
plane waves. Our main observation is that metrics with plane wave symmetry
satisfy every system of generally covariant vacuum field equations except the
Einstein equations. The proof uses the homothety admitted by metrics with plane
wave symmetry and the scaling behavior of generally covariant field equations.
We also discuss a mini-superspace description of spacetimes with plane wave
symmetry.Comment: 10 pages, TeX, uses IOP style file
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