Canonical Quantization of Two Dimensional Gauge Fields

$SU(N)$ gauge fields on a cylindrical spacetime are canonically quantized via two routes revealing almost equivalent but different quantizations. After removing all continuous gauge degrees of freedom, the canonical coordinate $A_\mu$ (in the Cartan subalgebra \h) is quantized. The compact route, as in lattice gauge theory, quantizes the Wilson loop $W$, projecting out gauge invariant wavefunctions on the group manifold $G$. After a Casimir energy related to the curvature of $SU(N)$ is added to the compact spectrum, it is seen to be a subset of the non-compact spectrum. States of the two quantizations with corresponding energy are shifted relative each other, such that the ground state on $G$, $\chi_0(W)$, is the first excited state $\Psi_1(A_\mu)$ on \h. The ground state $\Psi_0(A_\mu)$ does not appear in the character spectrum as its lift is not globally defined on $G$. Implications for lattice gauge theory and the sum over maps representation of two dimensional QCD are discussed.Comment: 32 pages, 3 figures uuencoded, Plain Te

Exploring Art Student Teachers’ Fictions of Teaching: Strategies for Teacher Educators

Using portions of my research involving three art student teachers, I provide suggestions for strategies to examine preservice art student teachers’ fictions about teaching (art). First, I begin by briefly introducing my three participants and listing my research methods. Next, I describe three of the most common teaching fictions I found through analyzation of the data. I discuss the productive usefulness, as well as a few procedures, of employing visual culture as a catalyst for unfolding student teachers’ (un)conscious pedagogical fictions. Then, I describe how creating illustrations of the self as art teacher can further help explore fictions of teaching. Lastly, I end by discussing how important it is to have a supportive space to talk and theorize with student teachers about their continuous processes of identity (re)formation and to work through the anxieties of the profession of teaching art

Hodge gauge fixing in three dimensions

A progress report on experiences with a gauge fixing method proposed in LATTICE 94 is presented. In this algorithm, an SU(N) operator is diagonalized at each site, followed by gauge fixing the diagonal (Cartan) part of the links to Coulomb gauge using the residual abelian freedom. The Cartan sector of the link field is separated into the physical gauge field $\alpha^{(f)}_\mu$ responsible for producing $f^{\rm Cartan}_{\mu\nu}$, the pure gauge part, lattice artifacts, and zero modes. The gauge transformation to the physical gauge field $\alpha^{(f)}_\mu$ is then constructed and performed. Compactness of the lattice fields entails issues related to monopoles and zero modes which are addressed.Comment: 4 pages Latex, 3 postscript figures, Poster presented at LATTICE96(topology

Gauge fixing and Gribov copies in pure Yang-Mills on a circle

%In order to understand how gauge fixing can be affected on the %lattice, we first study a simple model of pure Yang-mills theory on a %cylindrical spacetime [$SU(N)$ on $S^1 \times$ {\bf R}] where the %gauge fixed subspace is explicitly displayed. On the way, we find that %different gauge fixing procedures lead to different Hamiltonians and %spectra, which however coincide under a shift of states. The lattice %version of the model is compared and lattice gauge fixing issues are %discussed. (---TALK GIVEN AT LATTICE 92---AMSTERDAM, 15 SEPT. 92)Comment: 4 pages + 1 PostScript figure (appended), UVA-ITFA-92-34/ETH-IPS-92-22. --just archiving published versio

Two-flavour Schwinger model with dynamical fermions in the L\"uscher formalism

We report preliminary results for 2D massive QED with two flavours of Wilson fermions, using the Hermitean variant of L\"uscher's bosonization technique. The chiral condensate and meson masses are obtained. The simplicity of the model allows for high statistics simulations close to the chiral and continuum limit, both in the quenched approximation and with dynamical fermions.Comment: Talk presented at LATTICE96(algorithms), 3 pages, 3 Postscript figures, uses twoside, fleqn, espcrc2, epsf, revised version (details of approx. polynomial

Some Non-Perturbative Aspects of Gauge Fixing in Two Dimensional Yang-Mills Theory

Gauge fixing in general is incomplete, such that one solves some of the gauge constraints, quantizes, then imposes any residual gauge symmetries (Gribov copies) on the wavefunctions. While the Fadeev-Popov determinant keeps track of the local metric on this gauge fixed surface, the global topology of the reduced configuration space can be different depending on the treatment of the residual symmetries, which can in turn affect global properties of the theory such as the vacuum wavefunction. Pure $SU(N)$ gauge theory in two dimensions provides a simple yet non-trivial example where the above structure and effects can be elucidated explicitly, thus displaying physical effects of the treatment of Gribov copies.Comment: 3 pages (14.2kb), LaTeX + uufiles: 1 PS figure and sty file, Talk presented at LATTICE 93, ITFA-93-3

Smeared Gauge Fixing

We present a new method of gauge fixing to standard lattice Landau gauge, Max Re Tr $\sum_{\mu,x}U_{\mu,x}$, in which the link configuration is recursively smeared; these smeared links are then gauge fixed by standard extremization. The resulting gauge transformation is simultaneously applied to the original links. Following this preconditioning, the links are gauge fixed again as usual. This method is free of Gribov copies, and we find that for physical parameters ($\beta \geq 2$ in SU(2)), it generally results in the gauge fixed configuration with the globally maximal trace. This method is a general technique for finding a unique minimum to global optimization problems.Comment: 3 pages, 4 PostScript figures; Poster presented at LAT9

A Search for Pulsars Towards the Galactic Center

We present observations from two separate methods for observing the Galactic Center in an attempt to characterize its pulsar and neutron star populations. A persistent puzzle of the past 20 years has been the lack of pulsar detections towards the Galactic Center, specifically within a few parsecs of the central supermassive black hole Sgr A*. This object is bright in the total intensity of its polarized emission, but is very weakly linearly polarized. We take advantage of these circumstances in an experimental search technique where we utilize the Faraday effect in an attempt to detect high rotation measure (RM) point sources towards the Galactic Center, as the few pulsars that have been detected in this region have all been measured at a high RM. We also conduct a wide-field search of the 5◦area around the Galactic Center at low frequencies (230-470MHz) and at multiple epochs in an attempt to detect transient sources and other significant emitters of synchrotron radiation

Loop Correlators and Theta States in 2D Yang-Mills Theory

Explicit computations of the partition function and correlation functions of Wilson and Polyakov loop operators in theta-sectors of two dimensional Yang-Mills theory on the line cylinder and torus are presented. Several observations about the correspondence of two dimensional Yang-Mills theory with unitary matrix quantum mechanics are presented. The incorporation of the theta-angle which characterizes the states of two dimensional adjoint QCD is discussed.Comment: 30 pages, Latex, no figure