Gauge Consistent Wilson Renormalization Group I: Abelian Case

A version of the Wilson Renormalization Group Equation consistent with gauge symmetry is presented. A perturbative renormalizability proof is established. A wilsonian derivation of the Callan-Symanzik equation is given.Comment: Latex2e, 39 pages, 3 eps figures. Revised version to appear in Int. J. Mod. Phy

Is Quantum Einstein Gravity Nonperturbatively Renormalizable?

We find considerable evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity is ``asymptotically safe'' in Weinberg's sense. This would mean that the theory is likely to be nonperturbatively renormalizable and thus could be considered a fundamental (rather than merely effective) theory which is mathematically consistent and predictive down to arbitrarily small length scales. For a truncated version of the exact flow equation of the effective average action we establish the existence of a non-Gaussian renormalization group fixed point which is suitable for the construction of a nonperturbative infinite cutoff-limit. The truncation ansatz includes the Einstein-Hilbert action and a higher derivative term.Comment: 18 pages, latex, 3 figure

Effective Average Action in N=1 Super-Yang-Mills Theory

For N=1 Super-Yang-Mills theory we generalize the effective average action Gamma_k in a manifest supersymmetric way using the superspace formalism. The exact evolution equation for Gamma_k is derived and, introducing as an application a simple truncation, the standard one-loop beta-function of N=1 SYM theory is obtained.Comment: 17 pages, LaTeX, some remarks added, misprints corrected, to appear in Phys. Rev.

The effective action and quantum gauge transformations

The local symmetry transformations of the quantum effective action for general gauge theory are found. Additional symmetries arise under consideration of background gauges. Together with "trivial" gauge transformations, vanishing on mass shell, they can be used for construction simple gauge generators. For example, for the Yang-Mills theory the classically invariant effective action is obtained, reproducing DeWitt's result. For rank one theories a natural generalization is proposed.Comment: Revtex, 11 pages; added reference

Fragility of foot process morphology in kidney podocytes arises from chaotic spatial propagation of cytoskeletal instability

Kidney podocytes’ function depends on fingerlike projections (foot processes) that interdigitate with those from neighboring cells to form the glomerular filtration barrier. The integrity of the barrier depends on spatial control of dynamics of actin cytoskeleton in the foot processes. We determined how imbalances in regulation of actin cytoskeletal dynamics could result in pathological morphology. We obtained 3-D electron microscopy images of podocytes and used quantitative features to build dynamical models to investigate how regulation of actin dynamics within foot processes controls local morphology. We find that imbalances in regulation of actin bundling lead to chaotic spatial patterns that could impair the foot process morphology. Simulation results are consistent with experimental observations for cytoskeletal reconfiguration through dysregulated RhoA or Rac1, and they predict compensatory mechanisms for biochemical stability. We conclude that podocyte morphology, optimized for filtration, is intrinsically fragile, whereby local transient biochemical imbalances may lead to permanent morphological changes associated with pathophysiology

Scalar-QED \beta-functions near Planck's Scale

The Renormalization Group Flow Equations of the Scalar-QED model near Planck's scale are computed within the framework of the average effective action. Exact Flow Equations, corrected by Einstein Gravity, for the running self-interacting scalar coupling parameter and for the running v.e.v. of $\phi^* \phi$, are computed taking into account threshold effects. Analytic solutions are given in the infrared and ultraviolet limits.Comment: 19 pp, Latex; typos corrected and references added. To appear in the Int. J. Mod. Phys.