From Lattice Gauge Theories to Hydrogen Atoms

We construct canonical transformations to obtain a complete and most economical realization of the physical Hilbert space ${\cal H}^p$ of pure $SU(2)_{2+1}$ lattice gauge theory in terms of Wigner coupled Hilbert spaces of hydrogen atoms. One hydrogen atom is assigned to every plaquette of the lattice. A complete orthonormal description of the Wilson loop basis in ${\cal H}^p$ is obtained by all possible angular momentum Wigner couplings of hydrogen atom energy eigenstates $\vert n~l~m\rangle$ describing electric fluxes on the loops. The SU(2) gauge invariance implies that the total angular momenta of all hydrogen atoms vanish. The canonical transformations also enable us to rewrite the Kogut-Susskind Hamiltonian in terms of fundamental Wilson loop operators and their conjugate electric fields. The resulting loop Hamiltonian has a global SU(2) invariance and a simple weak coupling ($g^2\rightarrow 0$) continuum limit. The canonical transformations leading to the loop Hamiltonian are valid for any SU(N). The ideas and techniques can also be extended to higher dimension.Comment: 8 pages, 5 figures. minor typos corrected, minor changes in abstrac

Quark Wigner Distributions Using Light-Front Wave Functions

The quasi-probabilistic Wigner distributions are the quantum mechanical analog of the classical phase-space distributions. We investigate quark Wigner distributions for a quark state dressed with a gluon, which can be thought of as a simple composite and relativistic spin-1/2 state with a gluonic degree of freedom. We calculate various polarization configurations, namely unpolarized, longitudinally polarized and transversely polarized quark and the target state using light-front wave functions in this model. At leading twist, one can define 16 quark Wigner distributions, however, we obtain only 8 independent non-zero Wigner distributions in our model. We compare our results with other model calculations for the proton.Comment: 21 pages, 5 figures, version published by Phys. Rev.

Three Dimensional Imaging of the Nucleon

We study the Wigner distributions of quarks and gluons in light-front dressed quark model using the overlap of light front wave functions (LFWFs). We take the target to be a dressed quark, this is a composite spin $-1/2$ state of quark dressed with a gluon. This state allows us to calculate the quark and gluon Wigner distributions analytically in terms of LFWFs using Hamiltonian perturbation theory. We analyze numerically the Wigner distributions of quark and gluon and report their nature in the contour plots. We use an improved numerical technique to remove the cutoff dependence of the Fourier transformed integral over ${\bf \Delta}_\perp$.Comment: 7 pages, 2 figures, Prepared for Proceedings of Light Cone 2017, 18-22 Sept, University of Mumbai, India. To appear in FB

Wigner distributions of quarks for different polarizations

We calculate quark Wigner distributions using the light-front wave functions in a dressed quark model. In this model, a proton target is replaced by a simplified spin-1/2 state, namely a quark dressed with a gluon. We calculate the Wigner distributions for different polarization configuration of quark and the target state in this model.Comment: 6 pages, 12 figures. Presented by Jai More at Light Cone 2016, 5-8 September 2016, IST, Universidade de Lisboa, Portuga

Wigner Distributions For Gluons

We investigate the gluon Wigner distributions for unpolarized, longitudinally polarized and transversely polarized target state. Instead of a nucleon, we take the target state to be a quark dressed with a gluon at one loop and investigate the gluon Wigner distributions at leading twist. Better numerical convergence is obtained compared to an earlier study, that removes the regulator dependence of the results. We present a first calculation of the Wigner distribution for the transversely polarized target and linearly polarized gluon. We study the spin densities in momentum and impact parameter space. We also investigate the quark and gluon helicity and orbital angular momentum distributions at small-$x$.Comment: 27 pages, 10 figures, two figures added, replaced with the revised version published in EPJ

Optimization of Resistance Spot Welding Process Parameters using MOORA Approach

Optimization of resistance spot welding (RSW) process parameters was carried out to obtain optimal parametric combination to yield favourable weld nugget diameter, heat affected zone (HAZ) and breaking load in AISI 316 L austenitic stainless steel plates. Taguchi’s L16 orthogonal array (OA) design and signal- to- noise ratio (S/N ratio) have been used in this study. Weld nugget diameter, heat affected zone (HAZ) and breaking load are selected as objective functions. In this case the multi objective optimization on the basis of ratio analysis (MOORA) is applied to solve this multi objective, problem. MOORA in combination with standard deviation (SDV) was used for optimization process. Standard deviation (SDV) was used to determine the weights that were used for normalizing the responses obtained from the experimental results. It was found that welding current of 14 kA, welding time 14 cycle, electrode force 200Kgf and holding time 10 cycle produced the weldment with the best mechanical properties. This method can be used successfully in other welding applications