13,206 research outputs found
The Eight Dimensional Quantum Hall Effect and the Octonions
We construct a generalization of the quantum Hall effect where particles move
in an eight dimensional space under an SO(8) gauge field. The underlying
mathematics of this particle liquid is that of the last normed division
algebra, the octonions. Two fundamentally different liquids with distinct
configurations spaces can be constructed, depending on whether the particles
carry spinor or vector SO(8) quantum numbers. One of the liquids lives on a 20
dimensional manifold of with an internal component of SO(7) holonomy, whereas
the second liquid lives on a 14 dimensional manifold with an internal component
of holonomy.Comment: 5 page
A non-associative quantum mechanics
A non-associative quantum mechanics is proposed in which the product of three
and more operators can be non-associative one. The multiplication rules of the
octonions define the multiplication rules of the corresponding operators with
quantum corrections. The self-consistency of the operator algebra is proved for
the product of three operators. Some properties of the non-associative quantum
mechanics are considered. It is proposed that some generalization of the
non-associative algebra of quantum operators can be helpful for understanding
of the algebra of field operators with a strong interaction.Comment: one typo in Eq. (23) is correcte
ELECTROKINETIC PHENOMENA : VII. RELATIONSHIP BETWEEN ELECTRIC MOBILITY, CHARGE, TITRATION CURVE, AND OPTICAL ROTATION OF PROTEIN
The specific rotation of egg albumin, gliadin, and gelatin (40°C.) is discussed in connection with available data on (a) mobility, (b) titration curve, and (c) osmotic pressure. It seems likely that the change in specific rotation with pH of protein solutions is proportional to the change in net charge
Quark-Lepton Symmetry In Five Dimensions
We construct a complete five dimensional Quark-Lepton symmetric model, with
all fields propagating in the bulk. The extra dimension forms an orbifold with the zero mode fermions corresponding to standard model
quarks localised at one fixed point. Zero modes corresponding to
left(right)-chiral leptons are localised at (near) the other fixed point. This
localisation pattern is motivated by the symmetries of the model. Shifting the
right-handed neutrinos and charged leptons slightly from the fixed point
provides a new mechanism for understanding the absence of relations of the type
or in Quark-Lepton symmetric models. Flavour changing
neutral currents resulting from Kaluza Klein gluon exchange, which typically
arise in the quark sector of split fermion models, are suppressed due to the
localisation of quarks at one point. The separation of quarks and leptons in
the compact extra dimension also acts to suppress the proton decay rate. This
permits the extra dimension to be much larger than that obtained in a previous
construct, with the bound TeV obtained.Comment: 12 pages, references added to match published versio
Numerical studies of planar closed random walks
Lattice numerical simulations for planar closed random walks and their
winding sectors are presented. The frontiers of the random walks and of their
winding sectors have a Hausdorff dimension . However, when properly
defined by taking into account the inner 0-winding sectors, the frontiers of
the random walks have a Hausdorff dimension .Comment: 15 pages, 15 figure
CP Violation in \tau ->\nu\pi K_S and D->\pi K_S: The Importance of K_S-K_L Interference
The -factories have measured CP asymmetries in the and
modes. The state is identified by its decay to two pions at
a time that is close to the lifetime. Within the Standard Model and many
of its extensions, the asymmetries in these modes come from CP violation in
mixing. We emphasize that the interference between the
amplitudes of intermediate and is as important as the pure
amplitude. Consequently, the measured asymmetries depend on the times over
which the relevant decay rates are integrated and on features of the
experiment.Comment: 4 pages, 4 figure
B-Decay CP Asymmetries, Discrete Ambiguities and New Physics
The first measurements of CP violation in the system will likely probe
, and . Assuming that the CP angles
, and are the interior angles of the unitarity
triangle, these measurements determine the angle set
except for a twofold discrete ambiguity. If one allows for the possibility of
new physics, the presence of this discrete ambiguity can make its discovery
difficult: if only one of the two candidate solutions is consistent with
constraints from other measurements in the and systems, one is not sure
whether new physics is present or not. We review the methods used to resolve
the discrete ambiguity and show that, even in the presence of new physics, they
can usually be used to uncover this new physics. There are some exceptions,
which we describe in detail. We systematically scan the parameter space and
present examples of values of and the new-physics
parameters which correspond to all possibilities. Finally, we show that if one
relaxes the assumption that the bag parameters \BBd and \BK are positive,
one can no longer definitively establish the presence of new physics.Comment: 29 pages, LaTeX, 1 figures, presentation substantially reworked,
physics conclusions unchanged. This version will be published in Phys. Rev.
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