Generalized Spinfoams

We reconsider the spinfoam dynamics that has been recently introduced, in the generalized Kaminski-Kisielowski-Lewandowski (KKL) version where the foam is not dual to a triangulation. We study the Euclidean as well as the Lorentzian case. We show that this theory can still be obtained as a constrained BF theory satisfying the simplicity constraint, now discretized on a general oriented 2-cell complex. This constraint implies that boundary states admit a (quantum) geometrical interpretation in terms of polyhedra, generalizing the tetrahedral geometry of the simplicial case. We also point out that the general solution to this constraint (imposed weakly) depends on a quantum number r_f in addition to those of loop quantum gravity. We compute the vertex amplitude and recover the KKL amplitude in the Euclidean theory when r_f=0. We comment on the eventual physical relevance of r_f, and the formal way to eliminate it.Comment: 16 pages, 3 figure

Lofty pine and clinging vine: The educational 'Great Gatsby Curve' and the role of house prices

We investigate the heterogeneous and nonlinear intergenerational transmission channels of education and the impact on this of house price appreciation. Using the China Household Finance Survey 2011, we construct household history of property purchases and educational investment over the past 16 years with current filial educational achievement. Using quantile instrumental regressions, we find that through tightening households' credit constraints, rising house prices weaken the paternal intergenerational educational correlation by 38 per cent (from 0.366 to 0.226) but enhance the maternal correlation by 84 per cent (from 0.165 to 0.303). Decomposition analysis indicates the existence of glass-ceiling effects for females and rural offspring aiming to achieve high educational attainment due to narrower opportunities, and also glass-floor effects for urban offspring due to more endowment, which in turn leads to gender and urban-rural educational gaps across generations. The opportunity effect drives increasing intergenerational persistence of education over time