The Ward Identity from the Background Field Dependence of the Effective Action

The dependence of the effective action for gauge theories on the background field obeys an exact identity. We argue that for Abelian theories the Ward identity follows from the more general background field identity. This observation is particularly relevant for the anomalous Ward identity valid for gauge theories with an effective infrared cutoff as used for flow equations.Comment: 8 page

Sex hormones in allergic conjunctivitis: altered levels of circulating androgens and estrogens in children and adolescents with vernal keratoconjunctivitis

PURPOSE: Vernal keratoconjunctivitis (VKC) is a chronic allergic disease mainly affecting boys in prepubertal age and usually recovering after puberty. To evaluate a possible role of sex hormones in VKC, serum levels of sex hormones in children and adolescents with VKC were assessed. METHODS: 12 prepubertal and 7 early pubertal boys with active VKC and 6 male patients with VKC in remission phase at late pubertal age and 48 healthy age and sex-matched subjects were included. Serum concentration of estrone, 17 beta-estradiol, dehydroepiandrosterone-sulfate, total testosterone and free testosterone, dihydrotestosterone (DHT), cortisol, delta-4-androstenedione, follicle-stimulating hormone, luteinizing hormone, and sex-hormones binding globuline (SHBG) were evaluated. RESULTS: Serum levels of Estrone were significantly increased in all groups of patients with VKC when compared to healthy controls (P < 0.001). Prepubertal and early pubertal VKC showed a significant decrease in DHT (P = 0.007 and P = 0.028, resp.) and SHBG (P = 0.01 and P = 0.002, resp.) when compared to controls and serum levels of SHBG were increased in late pubertal VKC in remission phase (P = 0.007). CONCLUSIONS AND RELEVANCE: VKC patients have different circulating sex hormone levels in different phases of the disease and when compared to nonallergic subjects. These findings suggest a role played by sex hormones in the pathogenesis and/or activity of VKC

Topological invariants in interacting Quantum Spin Hall: a Cluster Perturbation Theory approach

Using Cluster Perturbation Theory we calculate Green's functions, quasi-particle energies and topological invariants for interacting electrons on a 2-D honeycomb lattice, with intrinsic spin-orbit coupling and on-site e-e interaction. This allows to define the parameter range (Hubbard U vs spin-orbit coupling) where the 2D system behaves as a trivial insulator or Quantum Spin Hall insulator. This behavior is confirmed by the existence of gapless quasi-particle states in honeycomb ribbons. We have discussed the importance of the cluster symmetry and the effects of the lack of full translation symmetry typical of CPT and of most Quantum Cluster approaches. Comments on the limits of applicability of the method are also provided.Comment: 7 pages, 7 figures: discussion improved, one figure added, references updated. Matches version published in New J. Phy

The beta functions of a scalar theory coupled to gravity

We study a scalar field theory coupled to gravity on a flat background, below Planck's energy. Einstein's theory is treated as an effective field theory. Within the context of Wilson's renormalization group, we compute gravitational corrections to the beta functions and the anomalous dimension of the scalar field, taking into account threshold effects.Comment: 13 pages, plainTe

Exact Flow Equations and the U(1)-Problem

The effective action of a SU(N)-gauge theory coupled to fermions is evaluated at a large infrared cut-off scale k within the path integral approach. The gauge field measure includes topologically non-trivial configurations (instantons). Due to the explicit infrared regularisation there are no gauge field zero modes. The Dirac operator of instanton configurations shows a zero mode even after the infrared regularisation, which leads to U_A(1)-violating terms in the effective action. These terms are calculated in the limit of large scales k.Comment: 22 pages, latex, no figures, with stylistic changes and some arguments streamlined, typos corrected, References added, to appear in Phys. Rev.

Periodic Instantons in SU(2) Yang-Mills-Higgs Theory

The properties of periodic instanton solutions of the classical SU(2) gauge theory with a Higgs doublet field are described analytically at low energies, and found numerically for all energies up to and beyond the sphaleron energy. Interesting new classes of bifurcating complex periodic instanton solutions to the Yang-Mills-Higgs equations are described.Comment: 11 pages, 3 figures (in 5 included eps files), ReVTeX (minor typos corrected and reference added

Evolution Equations for the Quark-Meson Transition

Evolution equations describe the effect of consecutively integrating out all quantum fluctuations with momenta larger than some infrared cutoff scale k. We develop a formalism for the introduction of collective degrees of freedom at some intermediate scale and derive the corresponding evolution equations. This allows to account for the appearance of bound states at some characteristic length scale as, for example, the mesons in QCD. The vacuum properties, including condensates of composite operators, can be directly infered from the effective action for k->0. We compute in a simple QCD-motivated model with four-quark interactions the chiral condensate \bar\psi\psi and the effective action for pions including f_\pi. A full treatment of QCD along these lines seems feasible but still requires substantial work. (5 figures available by ordinary mail upon request)Comment: 31 pages, HD-THEP-94-

Equation of state and coarse grained free energy for matrix models

We investigate phase transitions in three dimensional scalar matrix models, with special emphasis on complex $2 \times 2$ matrices. The universal equation of state for weak first order phase transitions is computed. We also study the coarse grained free energy. Its dependence on the coarse graining scale gives a quantitative criterion for the validity of the standard treatment of bubble nucleation.Comment: Latex, 48 page

Time evolution of correlation functions and thermalization

We investigate the time evolution of a classical ensemble of isolated periodic chains of O(N)-symmetric anharmonic oscillators. Our method is based on an exact evolution equation for the time dependence of correlation functions. We discuss its solutions in an approximation which retains all contributions in next-to-leading order in a 1/N expansion and preserves time reflection symmetry. We observe effective irreversibility and approximate thermalization. At large time the system approaches stationary solutions in the vicinity of, but not identical to, thermal equilibrium. The ensemble therefore retains some memory of the initial condition beyond the conserved total energy. Such a behavior with incomplete thermalization is referred to as "mesoscopic dynamics". It is expected for systems in a small volume. Surprisingly, we find that the nonthermal asymptotic stationary solutions do not change for large volume. This raises questions on Boltzmann's conjecture that macroscopic isolated systems thermalize.Comment: 40 pages, 9 figure