Gauge Theories on a Cylinder

(a few typos and an error corrected

QCD(1+1) with massless quarks and gauge covariant Sugawara construction

We use the Hamiltonian framework to study massless QCD$_{1+1}$, i.e.\ Yang-Mills gauge theories with massless Dirac fermions on a cylinder (= (1+1) dimensional spacetime $S^1\times \R$) and make explicite the full, non-perturbative structure of these quantum field theory models. We consider $N_F$ fermion flavors and gauge group either \U(N_C), \SU(N_C) or another Lie subgroup of \U(N_C). In this approach, anomalies are traced back to kinematical requirements such as positivity of the Hamiltonian, gauge invariance, and the condition that all observables are represented by well-defined operators on a Hilbert space. We also give equal time commutators of the energy momentum tensor and find a gauge-covariant form of the (affine-) Sugawara construction. This allows us to represent massless QCD$_{1+1}$ as a gauge theory of Kac-Moody currents and prove its equivalence to a gauged Wess-Zumino-Witten model with a dynamical Yang-Mills field.Comment: 11 pages, ESI 110 Minor changes (including title); version to appear in Phys. Lett.

The superfield quantisation of a superparticle action with an extended line element

A massive superparticle action based on the generalised line element in N = 1 global superspace is quantised canonically. A previous method of quantising this action, based on a Fock space analysis, showed that states existed in three supersymmetric multiplets, each of a different mass. The quantisation procedure presented uses the single first class constraint as an operator condition on a general N = 1 superwavefunction. The constraint produces coupled equations of motion for the component wavefunctions. Transformations of the component wavefunctions are derived that decouple the equations of motion and partition the resulting wavefunctions into three separate supermultiplets. Unlike previous quantisations of superparticle actions in N = 1 global superspace, the spinor wavefunctions satisfy the Dirac equation and the vector wavefunctions satisfy the Proca equation. The off-shell closure of the commutators of the supersymmetry transformations, that include mass parameters, are derived by the introduction of auxiliary wavefunctions. To avoid the ghosts arising in a previous Fock space quantisation an alternative conjugation is used in the definition of the current, based on a Krein space approach

Duality through the symplectic embedding formalism

In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method (NDM). We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method (SEM) is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the introduction of an explicit mass term and a topological term can be restored to obtain the dual equivalent and gauge-invariant version of the theory.Comment: RevTeX4, 10 pages. To appear in Int. J. Mod. Phys.

Three-dimensional mapping of fluorescent dye using a scanning, depth-resolving airborne lidar

Author Posting. © American Meteorological Society, 2007. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Atmospheric and Oceanic Technology 24 (2007): 1050-1065, doi:10.1175/JTECH2027.1.Results are presented from a pilot study using a fluorescent dye tracer imaged by airborne lidar in the ocean surface layer on spatial scales of meters to kilometers and temporal scales of minutes to hours. The lidar used here employs a scanning, frequency-doubled Nd:YAG laser to emit an infrared (1064 nm) and green (532 nm) pulse 6 ns in duration at a rate of 1 kHz. The received signal is split to infrared, green, and fluorescent (nominally 580–600 nm) channels, the latter two of which are used to compute absolute dye concentration as a function of depth and horizontal position. Comparison of dye concentrations inferred from the lidar with in situ fluorometry measurements made by ship shows good agreement both qualitatively and quantitatively for absolute dye concentrations ranging from 1 to >10 ppb. Uncertainties associated with horizontal variations in the natural seawater attenuation are approximately 1 ppb. The results demonstrate the ability of airborne lidar to capture high-resolution three-dimensional “snapshots” of the distribution of the tracer as it evolves over very short time and space scales. Such measurements offer a powerful observational tool for studies of transport and mixing on these scales.Support was provided by the Cecil H. and Ida M. Green Technology Innovation Fund under Grant 27001545, the Office of Naval Research Grant N00014-01-1-0984, and the Woods Hole Oceanographic Institution Coastal Ocean Institute

Path Integral Approach to Two-Dimensional QCD in the Light-Front

Two-dimensional quantum cromodynamics in the light-front frame is studied following hamiltonian methods. The theory is quantized using the path integral formalism and an effective theory similar to the Nambu-Jona Lasinio model is obtained. Confinement in two dimensions is derived analyzing directly the constraints in the path integral.Comment: 13pp, Plain-TeX, Si-93-10, IF-UFRJ-93-13, USM-TH-6

Asymptotic symmetry and conservation laws in 2d Poincar\'e gauge theory of gravity

The structure of the asymptotic symmetry in the Poincar\'e gauge theory of gravity in 2d is clarified by using the Hamiltonian formalism. The improved form of the generator of the asymptotic symmetry is found for very general asymptotic behaviour of phase space variables, and the related conserved quantities are explicitly constructed.Comment: 22 pages, Plain Te

Quantum Mechanics of Dynamical Zero Mode in QCD1+1QCD_{1+1} on the Light-Cone

Motivated by the work of Kalloniatis, Pauli and Pinsky, we consider the theory of light-cone quantized $QCD_{1+1}$ on a spatial circle with periodic and anti-periodic boundary conditions on the gluon and quark fields respectively. This approach is based on Discretized Light-Cone Quantization (DLCQ). We investigate the canonical structures of the theory. We show that the traditional light-cone gauge $A_- = 0$ is not available and the zero mode (ZM) is a dynamical field, which might contribute to the vacuum structure nontrivially. We construct the full ground state of the system and obtain the Schr\"{o}dinger equation for ZM in a certain approximation. The results obtained here are compared to those of Kalloniatis et al. in a specific coupling region.Comment: 19 pages, LaTeX file, no figure

The Teleparallel Lagrangian and Hamilton-Jacobi Formalism

We analyze the Teleparallel Equivalent of General Relativity (TEGR) from the point of view of Hamilton-Jacobi approach for singular systemsComment: 11 pages, no figures, to appear in GR

Dirac versus Reduced Quantization of the Poincar\'{e} Symmetry in Scalar Electrodynamics

The generators of the Poincar\'{e} symmetry of scalar electrodynamics are quantized in the functional Schr\"{o}dinger representation. We show that the factor ordering which corresponds to (minimal) Dirac quantization preserves the Poincar\'{e} algebra, but (minimal) reduced quantization does not. In the latter, there is a van Hove anomaly in the boost-boost commutator, which we evaluate explicitly to lowest order in a heat kernel expansion using zeta function regularization. We illuminate the crucial role played by the gauge orbit volume element in the analysis. Our results demonstrate that preservation of extra symmetries at the quantum level is sometimes a useful criterion to select between inequivalent, but nevertheless self-consistent, quantization schemes.Comment: 24 page