1,467 research outputs found
Helmut Karzel (1928-2021)
Obituary for Professor Dr. Dr. h.c. Helmut Karzel, who passed away on June
22, 2021, at the age of 93
Static interactions and stability of matter in Rindler space
Dynamical issues associated with quantum fields in Rindler space are
addressed in a study of the interaction between two sources at rest generated
by the exchange of scalar particles, photons and gravitons. These static
interaction energies in Rindler space are shown to be scale invariant, complex
quantities. The imaginary part will be seen to have its quantum mechanical
origin in the presence of an infinity of zero modes in uniformly accelerated
frames which in turn are related to the radiation observed in inertial frames.
The impact of a uniform acceleration on the stability of matter and the
properties of particles is discussed and estimates are presented of the
instability of hydrogen atoms when approaching the horizon.Comment: 28 pages, 4 figure
Global Left Loop Structures on Spheres
On the unit sphere in a real Hilbert space , we
derive a binary operation such that is a
power-associative Kikkawa left loop with two-sided identity ,
i.e., it has the left inverse, automorphic inverse, and properties. The
operation is compatible with the symmetric space structure of
. is not a loop, and the right translations
which fail to be injective are easily characterized.
satisfies the left power alternative and left Bol identities ``almost
everywhere'' but not everywhere. Left translations are everywhere analytic;
right translations are analytic except at where they have a
nonremovable discontinuity. The orthogonal group is a
semidirect product of with its automorphism group (cf.
http://www.arxiv.org/abs/math.GR/9907085). The left loop structure of
gives some insight into spherical geometry.Comment: 18 pages, no figures, 10pt, LaTeX2e, uses amsart.cls & tcilatex.tex.
To appear in Comment. Math. Univ. Carolin. (special issue: Proceedings of
LOOPS99) Revised version: various fixes and improvements suggested by refere
Unconventional string-like singularities in flat spacetime
The conical singularity in flat spacetime is mostly known as a model of the
cosmic string or the wedge disclination in solids. Its another, equally
important, function is to be a representative of quasiregular singularities.
From all these of views it seems interesting to find out whether there exist
other similar singularities. To specify what "similar" means I introduce the
notion of the string-like singularity, which is, roughly speaking, an
absolutely mild singularity concentrated on a curve or on a 2-surface S
(depending on whether the space is three- of four-dimensional). A few such
singularities are already known: the aforementioned conical singularity, two
its Lorentzian versions, the "spinning string", the "screw dislocation", and
Tod's spacetime. In all these spacetimes S is a straight line (or a plane) and
one may wonder if this is an inherent property of the string-like
singularities. The aim of this paper is to construct string-like singularities
with less trivial S. These include flat spacetimes in which S is a spiral, or
even a loop. If such singularities exist in nature (in particular, as an
approximation to gravitational field of strings) their cosmological and
astrophysical manifestations must differ drastically from those of the
conventional cosmic strings. Likewise, being realized as topological defects in
crystals such loops and spirals will probably also have rather unusual
properties.Comment: Draft. References and comments are welcome. v2. Section 3 is intact,
the rest is made briefer and clearer. A couple of references are added. v3.
Insignificant correstions. The published versio
Could the photon dispersion relation be non-linear ?
The free photon dispersion relation is a reference quantity for high
precision tests of Lorentz Invariance. We first outline theoretical approaches
to a conceivable Lorentz Invariance Violation (LIV). Next we address
phenomenological tests based on the propagation of cosmic rays, in particular
in Gamma Ray Bursts (GRBs). As a specific concept, which could imply LIV, we
then focus on field theory in a non-commutative (NC) space, and we present
non-perturbative results for the dispersion relation of the NC photon.Comment: 9 pages, 5 figures, talk presented at the 4. EU RTN Workshop on
"Constituents, Fundamental Forces and Symmetries of the Universe" in Varna,
Sept. 2008. References adde
The Rational Higher Structure of M-theory
We review how core structures of string/M-theory emerge as higher structures
in super homotopy theory; namely from systematic analysis of the brane bouquet
of universal invariant higher central extensions growing out of the superpoint.
Since super homotopy theory is immensely rich, to start with we consider this
in the rational/infinitesimal approximation which ignores torsion-subgroups in
brane charges and focuses on tangent spaces of super space-time. Already at
this level, super homotopy theory discovers all super -brane species, their
intersection laws, their M/IIA-, T- and S-duality relations, their black brane
avatars at ADE-singularities, including their instanton contributions, and,
last not least, Dirac charge quantization: for the D-branes it recovers twisted
K-theory, rationally, but for the M-branes it gives cohomotopy cohomology
theory. We close with an outlook on the lift of these results beyond the
rational/infinitesimal approximation to a candidate formalization of
microscopic M-theory in super homotopy theory.Comment: 32 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium
Higher Structures in M-Theory, August 201
Background Independent Quantum Gravity: A Status Report
The goal of this article is to present an introduction to loop quantum
gravity -a background independent, non-perturbative approach to the problem of
unification of general relativity and quantum physics, based on a quantum
theory of geometry. Our presentation is pedagogical. Thus, in addition to
providing a bird's eye view of the present status of the subject, the article
should also serve as a vehicle to enter the field and explore it in detail. To
aid non-experts, very little is assumed beyond elements of general relativity,
gauge theories and quantum field theory. While the article is essentially
self-contained, the emphasis is on communicating the underlying ideas and the
significance of results rather than on presenting systematic derivations and
detailed proofs. (These can be found in the listed references.) The subject can
be approached in different ways. We have chosen one which is deeply rooted in
well established physics and also has sufficient mathematical precision to
ensure that there are no hidden infinities. In order to keep the article to a
reasonable size, and to avoid overwhelming non-experts, we have had to leave
out several interesting topics, results and viewpoints; this is meant to be an
introduction to the subject rather than an exhaustive review of it.Comment: 125 pages, 5 figures (eps format), the final version published in CQ
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