DeWitt-Virasoro construction

We study a particular approach for analyzing worldsheet conformal invariance for bosonic string propagating in a curved background using hamiltonian formalism. We work in the Schrodinger picture of a single particle description of the problem where the particle moves in an infinite-dimensional space. Background independence is maintained in this approach by adopting DeWitt's (Phys.Rev.85:653-661,1952) coordinate independent formulation of quantum mechanics. This enables us to construct certain background independent notion of Virasoro generators, called DeWitt-Virasoro (DWV) generators, and invariant matrix elements of an arbitrary operator constructed out of them in spin-zero representation. We show that the DWV algebra is given by the Witt algebra with additional anomalous terms that vanish for Ricci-flat backgrounds. The actual quantum Virasoro generators should be obtained by first introducing the vacuum state and then normal ordering the DWV generators with respect to that. We demonstrate the procedure in the simple cases of flat and pp-wave backgrounds. This is a shorter version of arXiv:0912.3987 [hep-th] with many technical derivations omitted.Comment: 18 pages, shorter version of arXiv:0912.3987 [hep-th] accepted for publication in Pramana - Journal of Physic

Invariant solutions of the supersymmetric sine-Gordon equation

A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to the coefficients of the various powers of the anticommuting independent variables. Next, we consider the super-sine-Gordon equation expressed in terms of a bosonic superfield involving anticommuting independent variables. In each case, a Lie (super)algebra of symmetries is determined and a classification of all subgroups having generic orbits of codimension 1 in the space of independent variables is performed. The method of symmetry reduction is systematically applied in order to derive invariant solutions of the supersymmetric model. Several types of algebraic, hyperbolic and doubly periodic solutions are obtained in explicit form.Comment: 27 pages, major revision, the published versio

Galilei invariant theories. I. Constructions of indecomposable finite-dimensional representations of the homogeneous Galilei group: directly and via contractions

All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations are also obtained via contractions of the corresponding representations of the Lorentz group. Finally the obtained representations are used to derive a general Pauli anomalous interaction term and Darwin and spin-orbit couplings of a Galilean particle interacting with an external electric field.Comment: 23 pages, 2 table

On a coordinate independent description of string worldsheet theory

We study worldsheet conformal invariance for bosonic string propagating in a curved background using the hamiltonian formalism. In order to formulate the problem in a background independent manner we first rewrite the worldsheet theory in a language where it describes a single particle moving in an infinite-dimensional curved spacetime. This language is developed at a formal level without regularizing the infinite-dimensional traces. Then we adopt DeWitt's (Phys.Rev.85:653-661,1952) coordinate independent formulation of quantum mechanics in the present context. Given the expressions for the classical Virasoro generators, this procedure enables us to define the coordinate invariant quantum analogues which we call DeWitt-Virasoro generators. This framework also enables us to calculate the invariant matrix elements of an arbitrary operator constructed out of the DeWitt-Virasoro generators between two arbitrary scalar states. Using these tools we further calculate the DeWitt-Virasoro algebra in spin-zero representation. The result is given by the Witt algebra with additional anomalous terms that vanish for Ricci-flat backgrounds. Further analysis need to be performed in order to precisely relate this with the beta function computation of Friedan and others. Finally, we explain how this analysis improves the understanding of showing conformal invariance for certain pp-wave that has been recently discussed using hamiltonian framework.Comment: 32 pages, some reorganization for more elaborate explanation, no change in conclusio

Gauging the SU(2) Skyrme model

In this paper the SU(2) Skyrme model will be reformulated as a gauge theory and the hidden symmetry will be investigated and explored in the energy spectrum computation. To this end we purpose a new constraint conversion scheme, based on the symplectic framework with the introduction of Wess-Zumino (WZ) terms in an unambiguous way. It is a positive feature not present on the BFFT constraint conversion. The Dirac's procedure for the first-class constraints is employed to quantize this gauge invariant nonlinear system and the energy spectrum is computed. The finding out shows the power of the symplectic gauge-invariant formalism when compared with another constraint conversion procedures present on the literature.Comment: revised version, to appear in Phys.Rev.

The quantum superalgebra Uq[osp(1/2n)]U_q[osp(1/2n)]: deformed para-Bose operators and root of unity representations

We recall the relation between the Lie superalgebra $osp(1/2n)$ and para-Bose operators. The quantum superalgebra $U_q[osp(1/2n)]$, defined as usual in terms of its Chevalley generators, is shown to be isomorphic to an associative algebra generated by so-called pre-oscillator operators satisfying a number of relations. From these relations, and the analogue with the non-deformed case, one can interpret these pre-oscillator operators as deformed para-Bose operators. Some consequences for $U_q[osp(1/2n)]$ (Cartan-Weyl basis, Poincar\'e-Birkhoff-Witt basis) and its Hopf subalgebra $U_q[gl(n)]$ are pointed out. Finally, using a realization in terms of ``$q$-commuting'' $q$-bosons, we construct an irreducible finite-dimensional unitary Fock representation of $U_q[osp(1/2n)]$ and its decomposition in terms of $U_q[gl(n)]$ representations when $q$ is a root of unity.Comment: 15 pages, LaTeX (latex twice), no figure

Biofertilizantes y bioestimulantes para uso agrícola y acuícola: Bioprocesos aplicados a subproductos orgánicos de la industria pesquera

The development of products for human consumption with added value from hydrobiological resources generates remnants of the raw material that are classified as co-products, by-products and solid and liquid organic waste that, if not treated, cause a negative environmental impact. The use of these remnants for agricultural purposes is a reason for research because they have bioactive compounds and minerals of interest; Thus, the by-products have been used in bioprocesses that use eco-friendly methods such as aerobic biodegradation, fermentation, hydrolysis and extraction in the case of macroalgae. The products obtained from bioprocesses, depending on their composition of macronutrients, micronutrients, amino acids, microorganisms and bioactive compounds, can be considered as organic fertilizer and/or biostimulant, whose effect ranges from the improvement of growth and development in plants to the control of the biotic and abiotic stress in crops, so that they can grow without difficulties. Organic fertilizers derived from by-products and residual effluents from the fishing industry have adequate macronutrient (N, P and K) and micronutrient (Ca, Mg, S, B, Fe, Cu, Mn, Mo, Zn, and Cl) contents. for plants, as well as peptides and amino acids that are considered as biostimulants. On the other hand, the application of organic fertilizers and biostimulants covers various areas such as horticulture, hydroponics and live food production, the studies found indicated its potential use as a tool to implement organic agriculture and circular economy.El desarrollo de productos para consumo humano con valor agregado a partir de recursos hidrobiológicos genera remanentes de la materia prima que son clasificados como coproductos, subproductos y residuos orgánicos sólidos y líquidos que, si no son tratados, ocasionan un impacto ambiental negativo. El aprovechamiento de estos remanentes con fines agrícolas es motivo de investigación debido a que poseen compuestos bioactivos y minerales de interés; es así que los subproductos se vienen utilizando en bioprocesos que emplean métodos ecoamigables como la biodegradación aerobia, fermentación, hidrólisis y extracción en caso de las macroalgas. Los productos obtenidos de los bioprocesos, dependiendo de su composición de macronutrientes, micronutrientes, aminoácidos, microorganismos y compuestos bioactivos, puede ser considerado como fertilizante orgánico y/o bioestimulante, cuyo efecto abarca desde la mejora del crecimiento y desarrollo en plantas hasta el control del estrés biótico y abiótico en cultivos, de manera que puedan crecer sin dificultades. Los fertilizantes orgánicos derivados de los subproductos y efluentes residuales de la industria pesquera presentan adecuados contenidos de macronutrientes (N, P y K) y micronutrientes (Ca, Mg, S, B, Fe, Cu, Mn, Mo, Zn, y Cl) para las plantas, así como de péptidos y aminoácidos que son considerados como bioestimulantes. Por otro lado, la aplicación de fertilizantes orgánicos y bioestimulantes cubre diversas áreas como la horticultura, hidroponía y producción de alimento vivo, los estudios encontrados indicaron su potencial uso como herramienta para implementar la agricultura orgánica y economía circular

Algebraic structure of the Green's ansatz and its q-deformed analogue

The algebraic structure of the Green's ansatz is analyzed in such a way that its generalization to the case of q-deformed para-Bose and para-Fermi operators is becoming evident. To this end the underlying Lie (super)algebraic properties of the parastatistics are essentially used.Comment: plain TeX, Preprint INRNE-TH-94/4, 13

On the electrodynamics of moving bodies at low velocities

We discuss the seminal article in which Le Bellac and Levy-Leblond have identified two Galilean limits of electromagnetism, and its modern implications. We use their results to point out some confusion in the literature and in the teaching of special relativity and electromagnetism. For instance, it is not widely recognized that there exist two well defined non-relativistic limits, so that researchers and teachers are likely to utilize an incoherent mixture of both. Recent works have shed a new light on the choice of gauge conditions in classical electromagnetism. We retrieve Le Bellac-Levy-Leblond's results by examining orders of magnitudes, and then with a Lorentz-like manifestly covariant approach to Galilean covariance based on a 5-dimensional Minkowski manifold. We emphasize the Riemann-Lorenz approach based on the vector and scalar potentials as opposed to the Heaviside-Hertz formulation in terms of electromagnetic fields. We discuss various applications and experiments, such as in magnetohydrodynamics and electrohydrodynamics, quantum mechanics, superconductivity, continuous media, etc. Much of the current technology where waves are not taken into account, is actually based on Galilean electromagnetism

An Arabidopsis flavonoid transporter is required for anther dehiscence and pollen development

FLOWER FLAVONOID TRANSPORTER (FFT) encodes a multidrug and toxin efflux family transporter in Arabidopsis thaliana. FFT (AtDTX35) is highly transcribed in floral tissues, the transcript being localized to epidermal guard cells, including those of the anthers, stigma, siliques and nectaries. Mutant analysis demonstrates that the absence of FFT transcript affects flavonoid levels in the plant and that the altered flavonoid metabolism has wide-ranging consequences. Root growth, seed development and germination, and pollen development, release and viability are all affected. Spectrometry of mutant versus wild-type flowers shows altered levels of a glycosylated flavonol whereas anthocyanin seems unlikely to be the substrate as previously speculated. Thus, as well as adding FFT to the incompletely described flavonoid transport network, it is found that correct reproductive development in Arabidopsis is perturbed when this particular transporter is missing