Remark on Pauli-Villars Lagrangian on the Lattice

It is interesting to superimpose the Pauli-Villars regularization on the lattice regularization. We illustrate how this scheme works by evaluating the axial anomaly in a simple lattice fermion model, the Pauli-Villars Lagrangian with a gauge non-invariant Wilson term. The gauge non-invariance of the axial anomaly, caused by the Wilson term, is remedied by a compensation among Pauli-Villars regulators in the continuum limit. A subtlety in Frolov-Slavnov's scheme for an odd number of chiral fermions in an anomaly free complex gauge representation, which requires an infinite number of regulators, is briefly mentioned.Comment: 14 pages, Phyzzx. The final version to appear in Phys. Rev.

Manifestly Gauge Covariant Treatment of Lattice Chiral Fermion

We propose a lattice formulation of the chiral fermion which maximally respects the gauge symmetry and simultaneously is free of the unwanted species doublers. The formulation is based on the lattice fermion propagator and composite operators, rather than on the lattice fermion action. The fermionic determinant is defined as a functional integral of an expectation value of the gauge current operator with respect to the background gauge field: The gauge anomaly is characterized as the non-integrability. We perform some perturbative test to confirm the gauge covariance and an absence of the doublers. The formulation can be applied rather straightforwardly to numerical simulations in the quenched approximation.Comment: 11 pages, phyzzx, The final version to appear in Phys. Rev.

A New Look at the Axial Anomaly in Lattice QED with Wilson Fermions

By carrying out a systematic expansion of Feynman integrals in the lattice spacing, we show that the axial anomaly in the U(1) lattice gauge theory with Wilson fermions, as determined in one-loop order from an irrelevant lattice operator in the Ward identity, must necessarily be identical to that computed from the dimensionally regulated continuum Feynman integrals for the triangle diagrams.Comment: 1 figure, LaTeX, 18 page

Constraints on the Existence of Chiral Fermions in Interacting Lattice Theories

It is shown that an interacting theory, defined on a regular lattice, must have a vector-like spectrum if the following conditions are satisfied: (a)~locality, (b)~relativistic continuum limit without massless bosons, and (c)~pole-free effective vertex functions for conserved currents. The proof exploits the zero frequency inverse retarded propagator of an appropriate set of interpolating fields as an effective quadratic hamiltonian, to which the Nielsen-Ninomiya theorem is applied.Comment: LaTeX, 9 pages, WIS--93/56--JUNE--P

Normal origamis of Mumford curves

An origami (also known as square-tiled surface) is a Riemann surface covering a torus with at most one branch point. Lifting two generators of the fundamental group of the punctured torus decomposes the surface into finitely many unit squares. By varying the complex structure of the torus one obtains easily accessible examples of Teichm\"uller curves in the moduli space of Riemann surfaces. The p-adic analogues of Riemann surfaces are Mumford curves. A p-adic origami is defined as a covering of Mumford curves with at most one branch point, where the bottom curve has genus one. A classification of all normal non-trivial p-adic origamis is presented and used to calculate some invariants. These can be used to describe p-adic origamis in terms of glueing squares.Comment: 21 pages, to appear in manuscripta mathematica (Springer

Toward a script theory of guidance in computer-supported collaborative learning

This article presents an outline of a script theory of guidance for computer-supported collaborative learning (CSCL). With its four types of components of internal and external scripts (play, scene, role, and scriptlet) and seven principles, this theory addresses the question how CSCL practices are shaped by dynamically re-configured internal collaboration scripts of the participating learners. Furthermore, it explains how internal collaboration scripts develop through participation in CSCL practices. It emphasizes the importance of active application of subject matter knowledge in CSCL practices, and it prioritizes transactive over non-transactive forms of knowledge application in order to facilitate learning. Further, the theory explains how external collaboration scripts modify CSCL practices and how they influence the development of internal collaboration scripts. The principles specify an optimal scaffolding level for external collaboration scripts and allow for the formulation of hypotheses about the fading of external collaboration scripts. Finally, the article points towards conceptual challenges and future research questions

Manifestly Gauge Covariant Treatment of Lattice Chiral Fermions. II

We propose a new formulation of chiral fermions on a lattice, on the basis of a lattice extension of the covariant regularization scheme in continuum field theory. The species doublers do not emerge. The real part of the effective action is just one half of that of Dirac-Wilson fermion and is always gauge invariant even with a finite lattice spacing. The gauge invariance of the imaginary part, on the other hand, sets a severe constraint which is a lattice analogue of the gauge anomaly free condition. For real gauge representations, the imaginary part identically vanishes and the gauge invariance becomes exact.Comment: 15 pages, PHYZZX. The title is changed. The final version to appear in Phys. Rev.

The Evolution of Cosmic Magnetic Fields: From the Very Early Universe, to Recombination, to the Present

(abridged) A detailed examination of the evolution of stochastic magnetic fields between high cosmic temperatures and the present epoch is presented. A simple analytical model matching the results of the 3D MHD simulations allows for the prediction of present day magnetic field correlation lengths and energy. Our conclusions are multi fold. (a) Initial primordial fields with only a small amount of helicity are evolving into maximally helical fields. (b) There exists a correlation between the strength of the magnetic field, B, at the peak of it's spectrum and the location of the peak, given at the present epoch by: B ~ 5x10^{-12} (L/kpc) Gauss, where L is the correlation length determined by the initial magnetic field. (c) Concerning studies of generation of cosmic microwave background (CMBR) anisotropies due to primordial magnetic fields of B~10^{-9} Gauss on ~ 10 Mpc scales, such fields are not only impossible to generate in early causal magnetogenesis scenarios but also seemingly ruled out by distortions of the CMBR spectrum due to magnetic field dissipation on smaller scales and the overproduction of cluster magnetic fields. (d) The most promising detection possibility of CMBR distortions due to primordial magnetic fields may be on much smaller scales at higher multipoles l~10^6 where the signal is predicted to be the strongest. (e) It seems possible that magnetic fields in clusters of galaxies are entirely of primordial origin, without invoking dynamo amplification. Such fields would be of (pre-collapse) strength 10^{-12} - 10^{-11} Gauss with correlation lengths in the kpc range, and would also exist in voids of galaxies.Comment: 35 pages, 22 figures, revtex style, submitted to PR

A Perturbative Study of a General Class of Lattice Dirac Operators

A perturbative study of a general class of lattice Dirac operators is reported, which is based on an algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$ where $k$ stands for a non-negative integer. The choice $k=0$ corresponds to the commonly discussed Ginsparg-Wilson relation and thus to the overlap operator. We study one-loop fermion contributions to the self-energy of the gauge field, which are related to the fermion contributions to the one-loop $\beta$ function and to the Weyl anomaly. We first explicitly demonstrate that the Ward identity is satisfied by the self-energy tensor. By performing careful analyses, we then obtain the correct self-energy tensor free of infra-red divergences, as a general consideration of the Weyl anomaly indicates. This demonstrates that our general operators give correct chiral and Weyl anomalies. In general, however, the Wilsonian effective action, which is supposed to be free of infra-red complications, is expected to be essential in the analyses of our general class of Dirac operators for dynamical gauge field.Comment: 30 pages. Some of the misprints were corrected. Phys. Rev. D (in press

Experimental characterization of frequency dependent squeezed light

We report on the demonstration of broadband squeezed laser beams that show a frequency dependent orientation of the squeezing ellipse. Carrier frequency as well as quadrature angle were stably locked to a reference laser beam at 1064nm. This frequency dependent squeezing was characterized in terms of noise power spectra and contour plots of Wigner functions. The later were measured by quantum state tomography. Our tomograph allowed a stable lock to a local oscillator beam for arbitrary quadrature angles with one degree precision. Frequency dependent orientations of the squeezing ellipse are necessary for squeezed states of light to provide a broadband sensitivity improvement in third generation gravitational wave interferometers. We consider the application of our system to long baseline interferometers such as a future squeezed light upgraded GEO600 detector.Comment: 8 pages, 8 figure