Schwinger's Propagator Is Only A Green's Function

Schwinger used an analytic continuation of the effective action to correctly compute the particle production rate per unit volume for QED in a uniform electric field. However, if one simply evaluates the one loop expectation value of the current operator using his propagator, the result is zero! We analyze this curious fact from the context of a canonical formalism of operators and states. The explanation turns out to be that Schwinger's propagator is not actually the expectation value of the time-ordered product of field operators in the presence of a time-independent state, although it is of course a Green's function. We compute the true propagator in the presence of a state which is empty at $x_+ = 0$ where $x_+ \equiv (x^0+x^3)/\sqrt{2}$ is the lightcone evolution parameter. Our result can be generalized to electric fields which depend arbitrarily on $x_+$.Comment: 18 pages, LaTeX 2 epsilo

Degeneracy Structure of the Calogero-Sutherland Model: an Algebraic Approach

The degeneracy structure of the eigenspace of the N-particle Calogero-Sutherland model is studied from an algebraic point of view. Suitable operators satisfying SU(2) algebras and acting on the degenerate eigenspace are explicitly constructed for the two particle case and then appropriately generalized to the N-particle model. The raising and lowering operators of these algebras connect the states, in a subset of the degenerate eigenspace, with each other.Comment: 11 pages, REVTe

Cones of closed alternating walks and trails

Consider a graph whose edges have been colored red and blue. Assign a nonnegative real weight to every edge so that at every vertex, the sum of the weights of the incident red edges equals the sum of the weights of the incident blue edges. The set of all such assignments forms a convex polyhedral cone in the edge space, called the \emph{alternating cone}. The integral (respectively, $\{0,1\}$) vectors in the alternating cone are sums of characteristic vectors of closed alternating walks (respectively, trails). We study the basic properties of the alternating cone, determine its dimension and extreme rays, and relate its dimension to the majorization order on degree sequences. We consider whether the alternating cone has integral vectors in a given box, and use residual graph techniques to reduce this problem to searching for a closed alternating trail through a given edge. The latter problem, called alternating reachability, is solved in a companion paper along with related results.Comment: Minor rephrasing, new pictures, 14 page

Large nonlinear absorption and refraction coefficients of carbon nanotubes estimated from femtosecond Z-scan measurements

Nonlinear transmission of 80 and 140 femtosecond pulsed light with $0.79 \mu m$ wavelength through single walled carbon nanotubes suspended in water containing sodium dodecyl sulphate is studied. Pulse-width independent saturation absorption and negative cubic nonlinearity are observed, respectively, in open and closed aperture Z-scan experiments. The theoretical expressions derived to analyze the z-dependent transmission in the saturable limit require two photon absorption coefficient $\beta_0\sim$ $1.4 cm/MW$ and a nonlinear index $\gamma \sim -5.5 \times10^{-11} cm^2/W$ to fit the data.Comment: 10 pages, 2 figures. Accepted and to appear in Applied Physics Letter

Classification of Nonenzymatic Homologues of Protein Kinases

Protein Kinase-Like Non-kinases (PKLNKs), which are closely related to protein kinases, lack the crucial catalytic aspartate in the catalytic loop, and hence cannot function as protein kinase, have been analysed. Using various sensitive sequence analysis methods, we have recognized 82 PKLNKs from four higher eukaryotic organisms, namely, Homo sapiens, Mus musculus, Rattus norvegicus, and Drosophila melanogaster. On the basis of their domain combination and function, PKLNKs have been classified mainly into four categories: (1) Ligand binding PKLNKs, (2) PKLNKs with extracellular protein-protein interaction domain, (3) PKLNKs involved in dimerization, and (4) PKLNKs with cytoplasmic protein-protein interaction module. While members of the first two classes of PKLNKs have transmembrane domain tethered to the PKLNK domain, members of the other two classes of PKLNKs are cytoplasmic in nature. The current classification scheme hopes to provide a convenient framework to classify the PKLNKs from other eukaryotes which would be helpful in deciphering their roles in cellular processes

Impact response of composite materials

Composite materials composed of carbon fibers and resin matrices offer great promise in reducing the weight of aerospace structures. However they remain extremely vulnerable to out of plane impact loads, which lead to severe losses in strength and stiffness. The results of an experimental program, undertaken to investigate the low velocity impact damage tolerance of composite materials is presented. The objectives were to identify key neat resin/composite properties that lead to enhancement of composite impact damage tolerance and to find a small scale test that predicts compression after impact properties of panels. Five materials were selected for evaluation. These systems represented different classes of material behavior such as brittle epoxy, modified epoxies, and amorphous and semicrystalling thermoplastics. The influence of fiber properties on the impact performance was also studied in one material, i.e., in polyether ether ketone (PEEK). Several 24 and 48 ply quasi-isotropic and 24 ply orthotropic laminates were examined using an instrumented drop weight impactor. Correlations with post impact compression behavior were made

Analysis of By-Products of N2-SF6 Gas Mixtures Sparked under Inhomogenous Field Conditions

A vast data on formation of by-products due to arc and spark decomposition of SF6 is available in literature [1–10]. But experimental work relating to N2 - SF6 gas mixtures is limited. In view of increasing application of gas mixtures, it is essential to understand the nature of by-products formed in gas mixtures. Many recent studies have highlighted the advantages of using N2-SF6 gas mixtures as a replacement to SF6 gas for High Voltage application, with a view to reduce emission of SF6 gas into the atmosphere. Majority of these studies are aimed at determining the basic characteristics of N2-SF6 gas mixtures. However, this study attempts to understand the nature and quantum of different species formed in N2-SF6 mixtures in the presence of insulating spacers when sparked under inhomogeneous field conditions