102,602 research outputs found
Hamilton's theory of turns revisited
We present a new approach to Hamilton's theory of turns for the groups
SO(3) and SU(2) which renders their properties, in particular their
composition law, nearly trivial and immediately evident upon inspection.
We show that the entire construction can be based on binary rotations rather
than mirror reflections.Comment: 7 pages, 4 figure
Prophylactic Neutrality, Oppression, and the Reverse Pascal's Wager
In Beyond Neutrality, George Sher criticises the idea that state neutrality between competing conceptions of the good helps protect society from oppression. While he is correct that some governments are non-neutral without being oppressive, I argue that those governments may be neutral at the core of their foundations. The possibility of non-neutrality leading to oppression is further explored; some conceptions of the good would favour oppression while others would not. While it is possible that a non-neutral state may avoid oppression, it is argued that the risks are so great that it is better to bet on government being neutral, thereby minimizing the possibility of oppression
Hamilton's Turns for the Lorentz Group
Hamilton in the course of his studies on quaternions came up with an elegant
geometric picture for the group SU(2). In this picture the group elements are
represented by ``turns'', which are equivalence classes of directed great
circle arcs on the unit sphere , in such a manner that the rule for
composition of group elements takes the form of the familiar parallelogram law
for the Euclidean translation group. It is only recently that this construction
has been generalized to the simplest noncompact group , the double cover of SO(2,1). The present work develops a theory of
turns for , the double and universal cover of SO(3,1) and ,
rendering a geometric representation in the spirit of Hamilton available for
all low dimensional semisimple Lie groups of interest in physics. The geometric
construction is illustrated through application to polar decomposition, and to
the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late
Moments of the Wigner Distribution and a Generalized Uncertainty Principle
The nonnegativity of the density operator of a state is faithfully coded in
its Wigner distribution, and this places constraints on the moments of the
Wigner distribution. These constraints are presented in a canonically invariant
form which is both concise and explicit. Since the conventional uncertainty
principle is such a constraint on the first and second moments, our result
constitutes a generalization of the same to all orders. Possible application in
quantum state reconstruction using optical homodyne tomography is noted.Comment: REVTex, no figures, 9 page
Development of a 50 kW fluid transpiration arc solar simulator Final report
Development of 50 kW fluid transpiration arc solar simulato
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