5,468 research outputs found
Oriented Quantum Algebras and Coalgebras, Invariants of Oriented 1-1 Tangles, Knots and Links
In this paper we study oriented quantum coalgebras which are structures
closely related to oriented quantum algebras. We study the relationship between
oriented quantum coalgebras and oriented quantum algebras and the relationship
between oriented quantum coalgebras and quantum coalgebras. We show that there
are regular isotopy invariants of oriented 1-1 tangles and of oriented knots
and links associated to oriented and twist oriented quantum coalgebras
respectively. There are many parallels between the theory of oriented quantum
coalgebras and the theory of quantum coalgebra
Are Dark Energy and Dark Matter Different Aspects of the Same Physical Process?
It is suggested that the apparently disparate cosmological phenomena
attributed to so-called 'dark matter' and 'dark energy' arise from the same
fundamental physical process: the emergence, from the quantum level, of
spacetime itself. This creation of spacetime results in metric expansion around
mass points in addition to the usual curvature due to stress-energy sources of
the gravitational field. A recent modification of Einstein's theory of general
relativity by Chadwick, Hodgkinson, and McDonald incorporating spacetime
expansion around mass points, which accounts well for the observed galactic
rotation curves, is adduced in support of the proposal. Recent observational
evidence corroborates a prediction of the model that the apparent amount of
'dark matter' increases with the age of the universe. In addition, the proposal
leads to the same result for the small but nonvanishing cosmological constant,
related to 'dark energy, as that of the causet model of Sorkin et al.Comment: Some typos corrected. Comments welcome, pro or co
Oriented Quantum Algebras and Invariants of Knots and Links
In GT/0006019 oriented quantum algebras were motivated and introduced in a
natural categorical setting. Invariants of knots and links can be computed from
oriented quantum algebras, and this includes the Reshetikhin-Turaev theory for
Ribbon Hopf algebras. Here we continue the study of oriented quantum algebras
from a more algebraic perspective, and develop a more detailed theory for them
and their associated invariants.Comment: LAteX document, 45 pages, 17 figure
Taking Heisenberg's Potentia Seriously
It is argued that quantum theory is best understood as requiring an
ontological duality of res extensa and res potentia, where the latter is
understood per Heisenberg's original proposal, and the former is roughly
equivalent to Descartes' 'extended substance.' However, this is not a dualism
of mutually exclusive substances in the classical Cartesian sense, and
therefore does not inherit the infamous 'mind-body' problem. Rather, res
potentia and res extensa are proposed as mutually implicative ontological
extants that serve to explain the key conceptual challenges of quantum theory;
in particular, nonlocality, entanglement, null measurements, and wave function
collapse. It is shown that a natural account of these quantum perplexities
emerges, along with a need to reassess our usual ontological commitments
involving the nature of space and time.Comment: Final version, to appear in International Journal of Quantum
Foundation
Focal region fields of distorted reflectors
The problem of the focal region fields scattered by an arbitrary surface reflector under uniform plane wave illumination is solved. The physical optics (PO) approximation is used to calculate the current induced on the reflector. The surface of the reflector is described by a number of triangular domain-wise 5th degree bivariate polynomials. A 2-dimensional Gaussian quadrature is employed to numerically evaluate the integral expressions of the scattered fields. No Freshnel or Fraunhofer zone approximations are made. The relation of the focal fields problem to surface compensation techniques and other applications are mentioned. Several examples of distorted parabolic reflectors are presented. The computer code developed is included, together with instructions on its usage
SU(2) and the Kauffman bracket
A direct relationship between the (non-quantum) group SU(2) and the Kauffman
bracket in the framework of Chern-Simons theory is explicitly shown.Comment: 5 page
Chitinozoans in the subsurface Lower Paleozoic of West Texas
12 p., 16 pl., 4 fig.http://paleo.ku.edu/contributions.htm
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