Gauge Transformations, BRST Cohomology and Wigner's Little Group

We discuss the (dual-)gauge transformations and BRST cohomology for the two (1 + 1)-dimensional (2D) free Abelian one-form and four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theories by exploiting the (co-)BRST symmetries (and their corresponding generators) for the Lagrangian densities of these theories. For the 4D free 2-form gauge theory, we show that the changes on the antisymmetric polarization tensor e^{\mu\nu} (k) due to (i) the (dual-)gauge transformations corresponding to the internal symmetry group, and (ii) the translation subgroup T(2) of the Wigner's little group, are connected with each-other for the specific relationships among the parameters of these transformation groups. In the language of BRST cohomology defined w.r.t. the conserved and nilpotent (co-)BRST charges, the (dual-)gauge transformed states turn out to be the sum of the original state and the (co-)BRST exact states. We comment on (i) the quasi-topological nature of the 4D free 2-form gauge theory from the degrees of freedom count on e^{\mu\nu} (k), and (ii) the Wigner's little group and the BRST cohomology for the 2D one-form gauge theory {\it vis-{\`a}-vis} our analysis for the 4D 2-form gauge theory.Comment: LaTeX file, 29 pages, misprints in (3.7), (3.8), (3.9), (3.13) and (4.14)corrected and communicated to IJMPA as ``Erratum'

Geometrical Aspects Of BRST Cohomology In Augmented Superfield Formalism

In the framework of augmented superfield approach, we provide the geometrical origin and interpretation for the nilpotent (anti-)BRST charges, (anti-)co-BRST charges and a non-nilpotent bosonic charge. Together, these local and conserved charges turn out to be responsible for a clear and cogent definition of the Hodge decomposition theorem in the quantum Hilbert space of states. The above charges owe their origin to the de Rham cohomological operators of differential geometry which are found to be at the heart of some of the key concepts associated with the interacting gauge theories. For our present review, we choose the two $(1 + 1)$-dimensional (2D) quantum electrodynamics (QED) as a prototype field theoretical model to derive all the nilpotent symmetries for all the fields present in this interacting gauge theory in the framework of augmented superfield formulation and show that this theory is a {\it unique} example of an interacting gauge theory which provides a tractable field theoretical model for the Hodge theory.Comment: LaTeX file, 25 pages, Ref. [49] updated, correct page numbers of the Journal are give

Nilpotent Symmetries For Matter Fields In Non-Abelian Gauge Theory: Augmented Superfield Formalism

In the framework of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, the derivation of the (anti-)BRST nilpotent symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem. In our present investigation, the local, covariant, continuous and off-shell nilpotent (anti-)BRST symmetry transformations for the Dirac fields $(\psi, \bar\psi)$ are derived in the framework of the augmented superfield formulation where the four $(3 + 1)$-dimensional (4D) interacting non-Abelian gauge theory is considered on the six $(4 + 2)$-dimensional supermanifold parametrized by the four even spacetime coordinates $x^\mu$ and a couple of odd elements ($\theta$ and $\bar\theta$) of the Grassmann algebra. The requirement of the invariance of the matter (super)currents and the horizontality condition on the (super)manifolds leads to the derivation of the nilpotent symmetries for the matter fields as well as the gauge- and the (anti-)ghost fields of the theory in the general scheme of the augmented superfield formalism.Comment: LaTeX file, 16 pages, printing mistakes in the second paragraph of `Introduction' corrected, a footnote added, these modifications submitted as ``erratum'' to IJMPA in the final for

Adoption and impacts of zero tillage as a resource conserving technology in the irrigated plains of South Asia

Zero tillage / Rice / Wheat / Water conservation / India / Pakistan / Haryana / Punjab

Inflammatory Activity on Natalizumab Predicts Short-term but not Long-term Disability in Multiple Sclerosis

BACKGROUND: In people with multiple sclerosis treated with interferon-beta or glatiramer acetate, new MRI lesions and relapses during the first year of treatment predict a poor prognosis. OBJECTIVE: To study this association in those receiving natalizumab. METHODS: Data were collected on relapses, new MRI activity, and Modified Rio Score after initiation of natalizumab in an observational cohort of 161 patients with high baseline disability. These were correlated with Expanded Disability Status Scale (EDSS) progression at years 1, 2, 3, and 3-7 after treatment initiation, versus pre-treatment baseline. RESULTS: 46/161 patients had a relapse in the first year and 44/161 had EDSS progression by year 2. Relapses and Modified Rio Score in the first year of treatment predicted EDSS progression at year 1 and 2 after treatment initiation. However, this effect disappeared with longer follow-up. Paradoxically, there was a trend towards inflammatory activity on treatment (first year Modified Rio Score, relapses, and MRI activity) predicting a lower risk of EDSS progression by years 3-7, although this did not reach statistical significance. Those with and without EDSS progression did not differ in baseline age, EDSS, or pre-treatment relapse rate. Relapses in year 0-1 predicted further relapses in years 1-3. CONCLUSIONS: Breakthrough inflammatory activity after natalizumab treatment is predictive of short-term outcome measures of relapses or EDSS progression, but does not predict longer term EDSS progression, in this cohort with high baseline disability

Superfield Approach to (Non-)local Symmetries for One-Form Abelian Gauge Theory

We exploit the geometrical superfield formalism to derive the local, covariant and continuous Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations and the non-local, non-covariant and continuous dual-BRST symmetry transformations for the free Abelian one-form gauge theory in four $(3 + 1)$-dimensions (4D) of spacetime. Our discussion is carried out in the framework of BRST invariant Lagrangian density for the above 4D theory in the Feynman gauge. The geometrical origin and interpretation for the (dual-)BRST charges (and the transformations they generate) are provided in the language of translations of some superfields along the Grassmannian directions of the six ($4 + 2)$-dimensional supermanifold parametrized by the four spacetime and two Grassmannian variables.Comment: LaTeX file, 23 page

Contacting single bundles of carbon nanotubes with alternating electric fields

Single bundles of carbon nanotubes have been selectively deposited from suspensions onto sub-micron electrodes with alternating electric fields. We explore the resulting contacts using several solvents and delineate the differences between Au and Ag as electrode materials. Alignment of the bundles between electrodes occurs at frequencies above 1 kHz. Control over the number of trapped bundles is achieved by choosing an electrode material which interacts strongly with the chemical functional groups of the carbon nanotubes, with superior contacts being formed with Ag electrodes.Comment: 4 pages, RevTe

Magnetic phases evolution in the LaMn1-xFexO3+y system

We have investigated the crystal structure and magnetic properties for polycrystalline samples of LaMn1-xFexO3+y, in the whole range x=0.0 to x=1.0, prepared by solid state reaction in air. All samples show the ORT-2 orthorhombic structure that suppresses the Jahn-Teller distortion, thus favoring a ferromagnetic (FM) superexchange (SE) interaction between Mn^{3+}-O-Mn^{3+}. For x=0.0 the oxygen excess (y ~ 0.09) produces vacancies in the La and Mn sites and generates a fraction around 18% of Mn^{4+} ions and 82% of the usual Mn^{3+} ions, with possible double exchange interaction between them. The Fe doping in this system is known to produce only stable Fe^{3+} ions. We find an evolution from a fairly strong FM phase with a Curie temperature T_{C} ~ 160 K, for x=0.0, to an antiferromagnetic (AFM) phase with T_{N} = 790 K, for x=1.0, accompanied by clear signatures of a cluster-glass behavior. For intermediate Fe contents a mixed-phase state occurs, with a gradual decrease (increase) of the FM (AFM) phase, accompanied by a systematic transition broadening for 0.2 < x < 0.7. A model based on the expected exchange interaction among the various magnetic-ion types, accounts very well for the saturation-magnetization dependence on Fe doping.Comment: 27 pages, 9 figure

Effect of La Doping on Microstructure and Critical Current Density of MgB2

In the present study, La-doped MgB_2 superconductors with different doping level (Mg1-xLaxB2; x=0.00, 0.01, 0.03 & 0.05) have been synthesized by solid-state reaction route at ambient pressure. Effect of La doping have been investigated in relation to microstructural characteristics and superconducting properties, particularly intragrain critical current density (Jc). The microstructural characteristics of the as synthesized Mg(La)B2 compounds were studied employing transmission electron microscopic (TEM) technique. The TEM investigations reveal inclusion of LaB6 nanoparticles within the MgB2 grains which provide effective flux pinning centres. The evaluation of intragrain Jc through magnetic measurements on the fine powdered version of the as synthesized samples reveal that Jc of the samples change significantly with the doping level. The optimum result on Jc is obtained for Mg0.97La0.03B2 at 5K, the Jc reaches ~1.4x107A/cm2 in self field, ~2.1 x 106A/cm2 at 1T, ~2.5 x 105A/cm2 at 2.5T and ~1.8 x 104 A/cm2 at 4.5T. The highest value of intragrain Jc in Mg0.97La0.03B2 superconductor has been attributed to the inclusion of LaB6 nanoparticles which are capable of providing effective flux pinning centres

Comments on the dual-BRST symmetry

In view of a raging controversy on the topic of dual-Becchi-Rouet-Stora-Tyutin (dual-BRST/co-BRST) and anti-co-BRST symmetry transformations in the context of four (3+1)-dimensional (4D) Abelian 2-form and 2D (non-)Abelian 1-form gauge theories, we attempt, in our present short note, to settle the dust by taking the help of mathematics of differential geometry, connected with the Hodge theory, which was the original motivation for the nomenclature of "dual-BRST symmetry" in our earlier set of works. It has been claimed, in a recent set of papers, that the co-BRST symmetries are not independent of the BRST symmetries. We show that the BRST and co-BRST symmetries are independent symmetries in the same fashion as the exterior and co-exterior derivatives are independent entities belonging to the set of de Rham cohomological operators of differential geometry.Comment: LaTeX file, 6 pages, journal versio