Rigorous Limits on the Interaction Strength in Quantum Field Theory

We derive model-independent, universal upper bounds on the Operator Product Expansion (OPE) coefficients in unitary 4-dimensional Conformal Field Theories. The method uses the conformal block decomposition and the crossing symmetry constraint of the 4-point function. In particular, the OPE coefficient of three identical dimension $d$ scalar primaries is found to be bounded by ~ 10(d-1) for 1<d<1.7. This puts strong limits on unparticle self-interaction cross sections at the LHC.Comment: 11 pp, 3 figs + data file attache

Time decay of scaling critical electromagnetic Schr\"odinger flows

We obtain a representation formula for solutions to Schr\"odinger equations with a class of homogeneous, scaling-critical electromagnetic potentials. As a consequence, we prove the sharp $L^{1}\to L^{\infty}$ time decay estimate for the 3D-inverse square and the 2D-Aharonov-Bohm potentials.Comment: 32 pages, 1 figur

A Markovian and Roe-algebraic approach to asymptotic expansion in measure

In this paper, we conduct further studies on geometric and analytic properties of asymptotic expansion in measure. More precisely, we develop a machinery of Markov expansion and obtain an associated structure theorem for asymptotically expanding actions. Based on this, we establish an analytic characterisation for asymptotic expansion in terms of the Dru\c{t}u-Nowak projection and the Roe algebra of the associated warped cones. As an application, we provide new counterexamples to the coarse Baum-Connes conjecture