Faddeev-Jackiw canonical path integral quantization for a general scenario, its proper vertices and generating functionals

We generalize the Faddeev-Jackiw canonical path integral quantization for the scenario of a Jacobian with J=1 to that for the general scenario of non-unit Jacobian, give the representation of the quantum transition amplitude with symplectic variables and obtain the generating functionals of the Green function and connected Green function. We deduce the unified expression of the symplectic field variable functions in terms of the Green function or the connected Green function with external sources. Furthermore, we generally get generating functionals of the general proper vertices of any n-points cases under the conditions of considering and not considering Grassmann variables, respectively; they are regular and are the simplest forms relative to the usual field theory.

Dynamics of Vortex-Wave under a Travelling-Wave Modulation

The mecha nism of destabilization is studied for the rotating vortices (scroll waves and spiral waves) in excitable media induced by a parameter modulation in the form of a travelling-wave. It is found that a rigid rotating spiral in the two-dimensional (2D) system undergoes asynchronized drift along a straightline, and a 3D scrolling with its filament closed into a circle can be reoriented only if the direction of wavenumber of a travelling-wave perturbation is parallel to the ring plane. Then, in order to describe the behaviour of the synchronized drift of spiral wave and the reorientation of scrollring, the approximate formulas are given to exhibit qualitative agreements with the observed results.

Topological structure of vortex solution in Jackiw-Pi model

By using phi-mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortex solution and topological number, which is determined by Hopf index and Brouwer degree. We also give the quantization of flux in this case. Then, we study the angular momentum of the vortex, which can be expressed in terms of the flux.

BRST quantization and canonical Ward identity of the supersymmetric electromagnetic interaction system

According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian of the supersymmetric electromagnetic interaction system in phase space and the quantization procedure were simplified. The BRST generator was constructed, and the BRST transformations of supersymmetric fields were gotten; the effective action was calculated, and the generating functional for the Green function was achieved; also, the gauge generator was constructed, and the gauge transformation of the system was obtained. Finally, the Ward-Takahashi identities based on the canonical Noether theorem were calculated, and two relations between proper vertices and propagators were obtained.

Radiation-use efficiency and the harvest index of winter wheat at different nitrogen levels and their relationships to canopy spectral reflectance

Radiation-use efficiency (RUE, g/MJ) and the harvest index (HI, unitless) are two helpful characteristics in interpreting crop response to environmental and climatic changes. They are also increasingly important for accurate crop yield simulation, but they are affected by various environmental factors. In this study, the RUE and HI of winter wheat and their relationships to canopy spectral reflectance were investigated based on the massive field measurements of five nitrogen (N) treatments. Crop production can be separated into light interception and RUE. The results indicated that during a long period of slow growth from emergence to regreening, the effect of N on crop production mainly showed up in an increased light interception by the canopy. During the period of rapid growth from regreening to maturity, it was present in both light interception and RUE. The temporal variations of RUEAPAR (aboveground biomass produced per unit of photosynthetically active radiation absorbed by the canopy) during the period from regreening to maturity had different patterns corresponding to the N deficiency, N adequacy and N-excess conditions. Moreover, significant relationships were found between the RUEAPAR and the accumulative normalised difference vegetation index (NDVI) in the integrated season (R-2 = 0.68), between the HI and the accumulative NDVI after anthesis (R-2 = 0.89), and between the RUEgrain (ratio of grain yield to the total amount of photosynthetically active radiation absorbed by the canopy) and the accumulative NDVI of the whole season (R-2 = 0.89) and that after anthesis (R-2 = 0.94). It suggested that canopy spectral reflectance has the potential to reveal the spatial information of the RUEAPAR, HI and RUEgrain. It is hoped that this information will be useful in improving the accuracy of crop yield simulation in large areas.

Separation of ternary systems of hydrophilic ionic liquid with miscible organic compounds by RPLC with refractive index detection

A rapid and simple analytical method was developed for the simultaneous and quantitative determination and separation of hydrophilic imidazolium ionic liquids (ILs) (1-butyl-3-methylimidazolium chloride, [C(4)mim]Cl; 1-hexyl-3-methylimidazolium chloride, [C(6)mim]Cl; 1-octyl-3-methylimidazolium chloride, [C(8)mim]Cl; 1-allyl-3-methylimidazolium chloride, [Amim]Cl; or 1-allyl-3-methylimidazolium bromide, [Amim]Br) with miscible ethyl acetate and EtOH and their mixtures using reverse phase liquid chromatography coupled with refractive index detection (RPLC-RI). The influence of 60 to 100% (volume percentage) methanol in the mobile phase on the IL systems ([C(4)mim]Cl, [C(6)mim]Cl, [C(8)mim]Cl, [Amim]Br, or [Amim]Cl)-ethyl acetate-EtOH was investigated.