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

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

A new methodology called dice game optimizer for capacitor placement in distribution systems

Purpose. Shunt capacitors are installed in power system for compensating reactive power. Therefore, feeder capacity releases, voltage profile improves and power loss reduces. However, determination optimal location and size of capacitors in distributionsystems is a complex optimization problem. In order to determine the optimum size and location of the capacitor, an objective function which is generally defined based on capacitor installation costs and power losses should be minimized According to operational limitations. This paper offers a newly developed metaheuristic technique, named dice game optimizerto determine optimal size and location of capacitors in a distribution network. Dice game optimizer is a game based optimization technique that is based on the rules of the dice game.Цель. Шунтирующие конденсаторы в энергосистеме устанавливаются для компенсации реактивной мощности. Следовательно, снижается емкость фидера, улучшается профиль напряжения и снижаются потери мощности. Однако определение оптимального местоположения и размера конденсаторов в системах распределения является сложной задачей оптимизации. Чтобы определить оптимальный размер и расположение конденсатора, целевую функцию, которая обычно определяется на основе затрат на установку конденсатора и потерь мощности, следует минимизировать в соответствии с эксплуатационными ограничениями. Данная статья предлагает недавно разработанный метаэвристический метод, называемый оптимизатором игры в кости, для определения оптимального размера и расположения конденсаторов в распределительной сети. Оптимизатор игры в кости – это игровой метод оптимизации, основанный на правилах игры в кости

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

Fault diagnosis of rotor using EMD thresholding-based de-noising combined with probabilistic neural network

De-noising of signal processing is crucial for fault diagnosis in order to successfully conduct feature extraction and is an efficient method for accurate determination of cause. In this paper, the empirical mode decomposition (EMD) thresholding-based de-noising method and probabilistic neural network (PNN) are respectively used in the de-noising of the vibration signal and rotor fault diagnosis and compared with wavelet thresholding-based de-noising technology and back propagation neural network (BPNN). The results show that the clear iterative EMD interval thresholding performs better than wavelet thresholding in the de-noising of the vibration signal, and avoids the determination of wavelet basis and decomposition level. In addition, the PNN created by feature samples does not require training and has a higher accuracy than BPNN

Multiple model MIMO predictive control for variable speed variable pitch wind turbines

Abstract-A multivariable control strategy based on model predictive control techniques for the control of variable speed variable pitch wind turbines is proposed. The proposed control strategy is described for the whole operating region of the wind turbine (both partial and full load regimes). Pitch angle and generator torque are controlled simultaneously to maximize energy capture, mitigate drive train transient loads and smooth the power generated while reducing the pitch actuator activity. This has the effect of improving the efficiency and the power quality of the electrical power generated, and of increasing the life time of the system's mechanical parts. Furthermore, safe and acceptable operation of the system is guaranteed by incorporating most of the constraints on the physical variables of the WECS in the controller design. In order to cope with nonlinearities in the WECS and continuous variations in the operating point, a multiple model predictive controller is suggested which provides near optimal performance throughout the whole operating region