We provide a generalization of the horizontality condition of the usual superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to obtain the nilpotent (anti-)BRST symmetry transformations for all the fields of a four (3 + 1)-dimensional interacting 1-form U(1) gauge theory (QED) within the framework of the augmented superfield formalism. In the above interacting gauge theory, there i...

We derive together the exact local, covariant, continuous and off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the U(1) gauge field (Aμ), the (anti-)ghost fields ((C̄)C) and the Dirac fields (ψ, ψ̄) of the Lagrangian density of a four (3+1)-dimensional QED by exploiting a single restriction on the six (4, 2)dimensional supermanifold. A set of four ev...

Islamic arts are often identified by their abstract compositions based on geometric principles and spiritual concepts. Using artworks from different eras, this paper highlights the presence of a particular model of thought in Islamic arts in which the hierarchy of perspectival vision is abolished. The main argument is based on the ability of some artworks to be looked at from any angle while ma...

The BRST transformations for the Yang-Mills gauge fields in the presence of gravity with torsion are discussed by using the so-called Maurer-Cartan horizontality conditions. With the help of an operator δ which allows to decompose the exterior spacetime derivative as a BRST commutator we solve the Wess-Zumino consistency condition corresponding to invariant Chern-Simons terms and gauge anomalie...

This article provides the first comprehensive analysis of Finns Party’s (Perussuomalaiset [PS]) formal organisation and how it operates in practice. Following framework this thematic issue, to what extent does PS’s follow mass-party model centralised is party its internal decision-making? Analysis documents, association registries, in-depth interviews with 24 elite representatives reveal that P...

The use of sub-Riemannian geometry on the Heisenberg group H(n) provides a compact picture of symplectic geometry. Any Hamiltonian diffeomorphism on R lifts to a volume preserving bi-Lipschitz homeomorphisms of H(n), with the use of its generating function. Any curve of a flow of such homeomorphisms deviates from horizontality by the Hamiltonian of the flow. From the metric point of view this m...

islamic arts are often identified by their abstract compositions based on geometric principles and spiritual concepts. using artworks from different eras, this paper highlights the presence of a particular model of thought in islamic arts in which the hierarchy of perspectival vision is abolished. the main argument is based on the ability of some artworks to be looked at from any angle while ma...