Structural and Compositional Investigation of Pottery Samples from Guatemala

Purpose of investigation: The composition and characteristics of Mayan pottery samples from Guatemala was investigated

Circle actions, central extensions and string structures

The caloron correspondence can be understood as an equivalence of categories between $G$-bundles over circle bundles and $LG \rtimes_\rho S^1$-bundles where $LG$ is the group of smooth loops in $G$. We use it, and lifting bundle gerbes, to derive an explicit differential form based formula for the (real) string class of an $LG \rtimes_\rho S^1$-bundle.Comment: 25 page

Connectivity properties of moment maps on based loop groups

For a compact, connected, simply-connected Lie group G, the loop group LG is the infinite-dimensional Hilbert Lie group consisting of H^1-Sobolev maps S^1-->G. The geometry of LG and its homogeneous spaces is related to representation theory and has been extensively studied. The space of based loops Omega(G) is an example of a homogeneous space of $LG$ and has a natural Hamiltonian T x S^1 action, where T is the maximal torus of G. We study the moment map mu for this action, and in particular prove that its regular level sets are connected. This result is as an infinite-dimensional analogue of a theorem of Atiyah that states that the preimage of a moment map for a Hamiltonian torus action on a compact symplectic manifold is connected. In the finite-dimensional case, this connectivity result is used to prove that the image of the moment map for a compact Hamiltonian T-space is convex. Thus our theorem can also be viewed as a companion result to a theorem of Atiyah and Pressley, which states that the image mu(Omega(G)) is convex. We also show that for the energy functional E, which is the moment map for the S^1 rotation action, each non-empty preimage is connected.Comment: This is the version published by Geometry & Topology on 28 October 200

The use of disjunct eddy sampling methods for the determination of ecosystem level fluxes of trace gases

The concept of disjunct eddy sampling (DES) for use in measuring ecosystem-level micrometeorological fluxes is re-examined. The governing equations are discussed as well as other practical considerations and guidelines concerning this sampling method as it is applied to either the disjunct eddy covariance (DEC) or disjunct eddy accumulation (DEA) techniques. A disjunct eddy sampling system was constructed that could either be combined with relatively slow sensors (response time of 2 to 40 s) to measure fluxes using DEC, or could also be used to accumulate samples in stable reservoirs for later laboratory analysis (DEA technique). Both the DEC and DEA modes of this sampler were tested against conventional eddy covariance (EC) for fluxes of either CO2 (DEC) or isoprene (DEA). Good agreement in both modes was observed relative to the EC systems. However, the uncertainty in a single DEA flux measurement was considerable (40%) due to both the reduced statistical sampling and the analytical precision of the concentration difference measurements. We have also re-investigated the effects of nonzero mean vertical wind velocity on accumulation techniques as it relates to our DEA measurements. Despite the higher uncertainty, disjunct eddy sampling can provide an alternative technique to eddy covariance for determining ecosystem-level fluxes for species where fast sensors do not currently exist

Local Nature of Coset Models

The local algebras of the maximal Coset model C_max associated with a chiral conformal subtheory A\subset B are shown to coincide with the local relative commutants of A in B, provided A contains a stress energy tensor. Making the same assumption, the adjoint action of the unique inner-implementing representation U^A associated with A\subset B on the local observables in B is found to define net-endomorphisms of B. This property is exploited for constructing from B a conformally covariant holographic image in 1+1 dimensions which proves useful as a geometric picture for the joint inclusion A\vee C_max \subset B. Immediate applications to the analysis of current subalgebras are given and the relation to normal canonical tensor product subfactors is clarified. A natural converse of Borchers' theorem on half-sided translations is made accessible.Comment: 33 pages, no figures; typos, minor improvement

Annual Report 1965 Short Staple Cotton Breeding

This item is part of the Agricultural Experiment Station archive. It was digitized from a physical copy provided by the University Libraries at the University of Arizona. For more information, please email CALS Publications at [email protected]

String theories as the adiabatic limit of Yang-Mills theory

We consider Yang-Mills theory with a matrix gauge group $G$ on a direct product manifold $M=\Sigma_2\times H^2$, where $\Sigma_2$ is a two-dimensional Lorentzian manifold and $H^2$ is a two-dimensional open disc with the boundary $S^1=\partial H^2$. The Euler-Lagrange equations for the metric on $\Sigma_2$ yield constraint equations for the Yang-Mills energy-momentum tensor. We show that in the adiabatic limit, when the metric on $H^2$ is scaled down, the Yang-Mills equations plus constraints on the energy-momentum tensor become the equations describing strings with a worldsheet $\Sigma_2$ moving in the based loop group $\Omega G=C^\infty (S^1, G)/G$, where $S^1$ is the boundary of $H^2$. By choosing $G=R^{d-1, 1}$ and putting to zero all parameters in $\Omega R^{d-1, 1}$ besides $R^{d-1, 1}$, we get a string moving in $R^{d-1, 1}$. In arXiv:1506.02175 it was described how one can obtain the Green-Schwarz superstring action from Yang-Mills theory on $\Sigma_2\times H^2$ while $H^2$ shrinks to a point. Here we also consider Yang-Mills theory on a three-dimensional manifold $\Sigma_2\times S^1$ and show that in the limit when the radius of $S^1$ tends to zero, the Yang-Mills action functional supplemented by a Wess-Zumino-type term becomes the Green-Schwarz superstring action.Comment: 11 pages, v3: clarifying remarks added, new section on embedding of the Green-Schwarz superstring into d=3 Yang-Mills theory include

News from the Virasoro algebra

It is shown that the local quantum field theory of the chiral energy- momentum tensor with central charge $c=1$ coincides with the gauge invariant subtheory of the chiral $SU(2)$ current algebra at level 1, where the gauge group is the global $SU(2)$ symmetry. At higher level, the same scheme gives rise to $W$-algebra extensions of the Virasoro algebra.Comment: 4 pages, Latex, DESY 93-11

On Z-gradations of twisted loop Lie algebras of complex simple Lie algebras

We define the twisted loop Lie algebra of a finite dimensional Lie algebra $\mathfrak g$ as the Fr\'echet space of all twisted periodic smooth mappings from $\mathbb R$ to $\mathfrak g$. Here the Lie algebra operation is continuous. We call such Lie algebras Fr\'echet Lie algebras. We introduce the notion of an integrable $\mathbb Z$-gradation of a Fr\'echet Lie algebra, and find all inequivalent integrable $\mathbb Z$-gradations with finite dimensional grading subspaces of twisted loop Lie algebras of complex simple Lie algebras.Comment: 26 page

Generalized Particle Statistics in Two-Dimensions: Examples from the Theory of Free Massive Dirac Field

In the framework of algebraic quantum field theory we analyze the anomalous statistics exhibited by a class of automorphisms of the observable algebra of the two-dimensional free massive Dirac field, constructed by fermionic gauge group methods. The violation of Haag duality, the topological peculiarity of a two-dimensional space-time and the fact that unitary implementers do not lie in the global field algebra account for strange behaviour of statistics, which is no longer an intrinsic property of sectors. Since automorphisms are not inner, we exploit asymptotic abelianness of intertwiners in order to construct a braiding for a suitable $C^*$-tensor subcategory of End($\mathscr{A}$). We define two inequivalent classes of path connected bi-asymptopias, selecting only those sets of nets which yield a true generalized statistics operator.Comment: 24 page