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 $G_2$ 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 $S^1/Z_2\times Z_2'$ 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 $m_e=m_u$ or $m_e=m_d$ 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 $1/R\gtrsim30$ 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 $d_H=4/3$. However, when properly defined by taking into account the inner 0-winding sectors, the frontiers of the random walks have a Hausdorff dimension $d_H\approx 1.77$.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 $B$-factories have measured CP asymmetries in the $\tau\to\pi K_S\nu$ and $D\to K_S\pi$ modes. The $K_S$ state is identified by its decay to two pions at a time that is close to the $K_S$ lifetime. Within the Standard Model and many of its extensions, the asymmetries in these modes come from CP violation in $K^0-\bar{K}^0$ mixing. We emphasize that the interference between the amplitudes of intermediate $K_S$ and $K_L$ is as important as the pure $K_S$ 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 $B$ system will likely probe $\sin 2\alpha$, $\sin 2\beta$ and $\cos 2\gamma$. Assuming that the CP angles $\alpha$, $\beta$ and $\gamma$ are the interior angles of the unitarity triangle, these measurements determine the angle set $(\alpha,\beta,\gamma)$ 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 $B$ and $K$ 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 $(\alpha,\beta,\gamma)$ 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.