Einstein Manifolds As Yang-Mills Instantons

It is well-known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equations from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)_L instantons and SU(2)_R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.

Bell inequalities for three particles

We present tight Bell inequalities expressed by probabilities for three four- and five-dimensional systems. The tight structure of Bell inequalities for three $d$-dimensional systems (qudits) is proposed. Some interesting Bell inequalities of three qubits reduced from those of three qudits are also studied.Comment: 8 pages, 3 figures. Accepted for publication in Phys. Rev.

A Labelling Scheme for Higher Dimensional Simplex Equations

We present a succinct way of obtaining all possible higher dimensional generalization of Quantum Yang-Baxter Equation (QYBE). Using the scheme, we could generate the two popular three-simplex equations, namely: Zamolodchikov's tetrahedron equation (ZTE) and Frenkel and Moore equation (FME).Comment: To appear as a Letter to the Editor in J. Phys. A:Math and Ge

The Peculiar Velocity Function of Galaxy Clusters

The peculiar velocity function of clusters of galaxies is determined using an accurate sample of cluster velocities based on Tully-Fisher distances of Sc galaxies (Giovanelli et al 1995b). In contrast with previous results based on samples with considerably larger velocity uncertainties, the observed velocity function does not exhibit a tail of high velocity clusters. The results indicate a low probability of $\lesssim$\,5\% of finding clusters with one-dimensional velocities greater than $\sim$ 600 {\kms}. The root-mean-square one-dimensional cluster velocity is 293$\pm$28 {\kms}. The observed cluster velocity function is compared with expectations from different cosmological models. The absence of a high velocity tail in the observed function is most consistent with a low mass-density ($\Omega \sim$0.3) CDM model, and is inconsistent at $\gtrsim 3 \sigma$ level with $\Omega$= 1.0 CDM and HDM models. The root-mean-square one-dimensional cluster velocities in these models correspond, respectively, to 314, 516, and 632 {\kms} (when convolved with the observational uncertainties). Comparison with the observed RMS cluster velocity of 293$\pm$28 {\kms} further supports the low-density CDM model.Comment: revised version accepted for publication in ApJ Letters, 18 pages, uuencoded PostScript with 3 figures included; complete paper available through WWW at http://www.astro.princeton.edu/~library/prep.htm

Dynamics of quantum-classical hybrid system: effect of matter-wave pressure

Radiation pressure affects the kinetics of a system exposed to the radiation and it constitutes the basis of laser cooling. In this paper, we study {\it matter-wave pressure} through examining the dynamics of a quantum-classical hybrid system. The quantum and classical subsystem have no explicit coupling to each other, but affect mutually via a changing boundary condition. Two systems, i.e., an atom and a Bose-Einstein condensate(BEC), are considered as the quantum subsystems, while an oscillating wall is taken as the classical subsystem. We show that the classical subsystem would experience a force proportional to $Q^{-3}$ from the quantum atom, whereas it acquires an additional force proportional to $Q^{-2}$ from the BEC due to the atom-atom interaction in the BEC. These forces can be understood as the {\it matter-wave pressure}.Comment: 7 pages, 6 figue