Time-independant stochastic quantization, DS equations, and infrared critical exponents in QCD

We derive the equations of time-independent stochastic quantization, without reference to an unphysical 5th time, from the principle of gauge equivalence. It asserts that probability distributions $P$ that give the same expectation values for gauge-invariant observables $= \int dA W P$ are physically indistiguishable. This method escapes the Gribov critique. We derive an exact system of equations that closely resembles the Dyson-Schwinger equations of Faddeev-Popov theory, which we then solve non-perturbatively for the critical exponents that characterize the asymptotic form at $k \approx 0$ of the tranverse and longitudinal parts of the gluon propagator in Landau gauge, D^T \sim (k^2)^{-1-\a_T} and D^L \sim a (k^2)^{-1-\a_L}, and obtain \a_T = - 2\a_L \approx - 1.043 (short range), and \a_L \approx 0.521, (long range). Although the longitudinal part vanishes with the gauge parameter $a$ in the Landau gauge limit, $a \to 0$, there are vertices of order $a^{-1}$, so the longitudinal part of the gluon propagator contributes in internal lines, replacing the ghost that occurs in Faddeev-Popov theory. We compare our results with the corresponding results in Faddeev-Popov theory.Comment: 50 pages, 2 figure

Polycomb Repressive Complex 2 Controls the Embryo-to-Seedling Phase Transition

Polycomb repressive complex 2 (PRC2) is a key regulator of epigenetic states catalyzing histone H3 lysine 27 trimethylation (H3K27me3), a repressive chromatin mark. PRC2 composition is conserved from humans to plants, but the function of PRC2 during the early stage of plant life is unclear beyond the fact that it is required for the development of endosperm, a nutritive tissue that supports embryo growth. Circumventing the requirement of PRC2 in endosperm allowed us to generate viable homozygous null mutants for FERTILIZATION INDEPENDENT ENDOSPERM (FIE), which is the single Arabidopsis homolog of Extra Sex Combs, an indispensable component of Drosophila and mammalian PRC2. Here we show that H3K27me3 deposition is abolished genome-wide in fie mutants demonstrating the essential function of PRC2 in placing this mark in plants as in animals. In contrast to animals, we find that PRC2 function is not required for initial body plan formation in Arabidopsis. Rather, our results show that fie mutant seeds exhibit enhanced dormancy and germination defects, indicating a deficiency in terminating the embryonic phase. After germination, fie mutant seedlings switch to generative development that is not sustained, giving rise to neoplastic, callus-like structures. Further genome-wide studies showed that only a fraction of PRC2 targets are transcriptionally activated in fie seedlings and that this activation is accompanied in only a few cases with deposition of H3K4me3, a mark associated with gene activity and considered to act antagonistically to H3K27me3. Up-regulated PRC2 target genes were found to act at different hierarchical levels from transcriptional master regulators to a wide range of downstream targets. Collectively, our findings demonstrate that PRC2-mediated regulation represents a robust system controlling developmental phase transitions, not only from vegetative phase to flowering but also especially from embryonic phase to the seedling stage