Superfield Approach to Nilpotency and Absolute Anticommutativity of Conserved Charges: 2D non-Abelian 1-Form Gauge Theory

We exploit the theoretical strength of augmented version of superfield approach (AVSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism to express the nilpotency and absolute anticommutativity properties of the (anti-)BRST and (anti-)co-BRST conserved charges for the two $(1+1)$-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields) in the language of superspace variables, their derivatives and suitable superfields. In the proof of absolute anticommutativity property, we invoke the strength of Curci-Ferrari (CF) condition for the (anti-)BRST charges. No such outside condition/restriction is required in the proof of absolute anticommutativity of the (anti-)co-BRST conserved charges. The latter observation (as well as other observations) connected with (anti-)co-BRST symmetries and corresponding conserved charges are novel results of our present investigation. We also discuss the (anti-)BRST and (anti-)co-BRST symmetry invariance of the appropriate Lagrangian densities within the framework of AVSA. In addition, we dwell a bit on the derivation of the above fermionic (nilpotent) symmetries by applying the AVSA to BRST formaism where only the (anti-)chiral superfields are used.Comment: LaTeX file, 33 pages, journal referenc

Modified 2D Proca Theory: Revisited Under BRST and (Anti-)Chiral Superfield Formalisms

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) approach, we discuss mainly the fermionic (i.e. off-shell nilpotent) (anti-)BRST, (anti-)co-BRST and some discrete dual-symmetries of the appropriate Lagrangian densities for a two (1+1)-dimensional (2D) modified Proca (i.e. a massive Abelian 1-form) theory without any interaction with matter fields. One of the novel observations of our present investigation is the existence of some kinds of restrictions in the case of our present St\"{u}ckelberg-modified version of the 2D Proca theory which is not like the standard Curci-Ferrari (CF)-condition of a non-Abelian 1-form gauge theory. Some kinds of similarities and a few differences between them have been pointed out in our present investigation. To establish the sanctity of the above off-shell nilpotent (anti-)BRST and (anti-)co-BRST symmetries, we derive them by using our newly proposed (anti-)chiral superfield formalism where a few specific and appropriate sets of invariant quantities play a decisive role. We express the (anti-)BRST and (anti-)co-BRST conserved charges in terms of the superfields that are obtained after the applications of (anti-)BRST and (anti-)co-BRST invariant restrictions and prove their off-shell nilpotency and absolute anticommutativity properties, too. Finally, we make some comments on (i) the novelty of our restrictions/obstructions, and (ii) the physics behind the negative kinetic term associated with the pseudo-scalar field of our present theory.Comment: LaTeX file, 58 pages, Journal reference give

QQˉQ\bar Q (Q∈{b,c}Q\in \{b, c\}) spectroscopy using Cornell potential

The mass spectra and decay properties of heavy quarkonia are computed in nonrelativistic quark-antiquark Cornell potential model. We have employed the numerical solution of Schr\"odinger equation to obtain their mass spectra using only four parameters namely quark mass ($m_c$, $m_b$) and confinement strength ($A_{c\bar c}$, $A_{b\bar b}$). The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are computed perturbatively to determine the mass spectra of excited $S$, $P$, $D$ and $F$ states. Digamma, digluon and dilepton decays of these mesons are computed using the model parameters and numerical wave functions. The predicted spectroscopy and decay properties for quarkonia are found to be consistent with available experimental observations and results from other theoretical models. We also compute mass spectra and life time of the $B_c$ meson without additional parameters. The computed electromagnetic transition widths of heavy quarkonia and $B_c$ mesons are in tune with available experimental data and other theoretical approaches

Benefit of irrigation water transfers in the National River Linking Project: a case study of the Ken-Betwa link

River basin managementRiver basin developmentDevelopment projectsWater transferIrrigation waterCrop productionCrop managementLivestock

Development of 2024 p/m aluminium alloy–SiCp nanocomposites via mechanical alloying

Aluminum alloy 2024 is the best known most widely used aircraft structural alloy. Now a days it is also gaining ground in automotive industry. In the present studies, 2024 P/M Al alloy and SiC particulates have been chosen as matrix and reinforcement materials, respectively. Mechanical alloying (MA) was used to obtain uniform SiCp dispersion in the matrix. MA powder was vacuum degassed and consolidated by hot pressing and subsequent hot forging. Thereafter the composites were heat treated to give T-6 temper. Optical and scanning electron microscopy of the composite was carried out and evaluation of mechanical properties was done. The principal objective of the present investigations was to determine how the particulate volume fraction and extent of mechanical alloying affect the microstructure and tensile properties of 2024 P/M Al alloy-SiCp composites. In these efforts it could be possible to develop nano composites of 2024 P/M Al alloy-SiCp having tensile strength of 504 MPa and modulus of elasticity of 105 GPa

Constraints, Symmetry Transformations and Conserved Charges for Massless Abelian 3-Form Theory

We demonstrate the existence of the first-class constraints on the massless Abelian 3-form theory which generate the classical gauge symmetry transformations for this theory in any arbitrary D-dimension of spacetime. We write down the explicit expression for the generator in terms of these first-class constraints. Using the celebrated Noether theorem, corresponding to the gauge symmetry transformations, we derive the Noether conserved current and conserved charge. The latter is connected with the first-class constraints of the theory in a subtle manner as we demonstrate clearly in our present investigation. We comment on the first-class constraints within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism where the conserved (anti-)BRST charges are the generalizations of the above generator for the classical gauge symmetry transformations. The standard Noether conserved (anti-)BRST charges are found to be non-nilpotent. We derive the nilpotent versions of the (anti-)BRST charges. One of the interesting observations of our present endeavor is the result that only the nilpotent versions of the conserved (anti-)BRST charges lead to the annihilation of the physical states by the operator form of the first-class constraints at the quantum level which is consistent with the Dirac quantization condition for the systems that are endowed with any kind of constraints.Comment: LaTeX file, 15 pages v2: major changes in the title and text, references expanded, 21 page

Polymer-clay Nano Composites

Nano has now become a theme in almost all the established discipline. The confluence ofinnovative methodologies, sophisticated characterisation techniques, and potential technologicalutility has resulted in intense research activity in the field of polymer nano composites. Polymercomposites made out of nano materials display unique properties in terms of improved tensilestrength, flexibility, and flexural endurance. The paper discusses the development of polymerclaynano composites, both from the conceptual point of view as well as practical methods forthe synthesis of nano composites. These are monomer intercalation, monomer modification,common solvent, and melt-intercalation methods. Various models have been discussed thatdescribe improvements in mechanical and barriers properties due to the incorporation of nanomaterials. Ongoing R&D work in the two DRDO laboratories on the development of nanocomposites has been briefly mentioned. The emerging use of polymer-nano composites has alsobeen described