We present a brief review of the cohomological solutions of self-coupling interactions of the fields in the free Yang-Mills theory. All consistent interactions among the fields have been obtained using the antifield formalism through several order BR
ST deformations of the master equation. It is found that the coupling deformations halt exclusively at the second order, whereas higher order deformations are obstructed due to non-local interactions. The results demonstrate the BRST cohomological derivation of the interacting Yang-Mills theory.
The Weyl curvature includes the Newtonian field and an additional field, the so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci identities to provide a set of constraints and propagations for the Weyl fields. The temporal evolution
s of propagations manifest explicit solutions of gravitational waves. We see that models with purely Newtonian field are inconsistent with relativistic models and obstruct sounding solutions. Therefore, both fields are necessary for the nonlocal nature and radiative solutions of gravitation.
We have used the Wide Field Spectrograph on the Australian National University 2.3-m telescope to perform the integral field spectroscopy for a sample of the Galactic planetary nebulae. The spatially resolved velocity distributions of the H$alpha$ em
ission line were used to determine the kinematic features and nebular orientations. Our findings show that some bulge planetary nebulae toward the Galactic center have a particular orientation.
