We discuss some aspects of the topological features of a non-interacting two (1 + 1)-dimensional Abelian gauge theory in the framework of superfield formalism. This theory is described by a BRST invariant Lagrangian density in the Feynman gauge. We express the local and continuous symmetries, Lagrangian density, topological invariants and symmetric energy momentum tensor of this theory in the l...

In the framework of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, the derivation of the (anti-)BRST nilpotent symmetry transformations 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 D...

We study topological Yang-Mills-Higgs theories in two and three dimensions and topological Yang-Mills theory in four dimensions in a unified framework of superconnections. In this framework, we first show that a classical action of topological Yang-Mills type can provide all three classical actions of these theories via appropriate projections. Then we obtain the BRST and anti-BRST transformati...

Theorem. Any compact Riemann surface may be minimally immersed in S. To prove this, Bryant considers the Penrose fibration π : CP 3 → S = HP . The perpendicular complement to the fibres (with respect to the Fubini-Study metric) furnishes CP 3 with a holomorphic distribution H ⊂ T CP 3 and it is well-known that a holomorphic curve in CP 3 tangent to H (a horizontal holomorphic curve) projects on...

In the framework of superfield approach, we derive the local, covariant, continuous and nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations on the U(1) gauge field (Aμ) and the (anti-)ghost fields ((C̄)C) of the Lagrangian density of the two (1 + 1)-dimensional QED by exploiting the (dual-)horizontality conditions defined on the four (2+2)-dimensional supermanifold. The long-standi...

BACKGROUND We have observed that dry eye redness is characterized by a prominence of fine horizontal conjunctival vessels in the exposed ocular surface of the interpalpebral fissure, and have incorporated this feature into the grading of redness in clinical studies of dry eye. AIM To develop an automated method of grading dry eye-associated ocular redness in order to expand on the clinical gr...

Some of the key cohomological features of the two (1+1)-dimensional (2D) free Abelianand self-interacting non-Abelian gauge theories (having no interaction with matter fields) are briefly discussed first in the language of symmetry properties of the Lagrangian densities and the same issues are subsequently addressed in the framework of superfield formulation on the four (2+ 2)-dimensional super...

In the framework of usual superfield approach, we derive the exact local, covari-ant, continuous and off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the U(1) gauge field (A µ) and the (anti-)ghost fields ((¯ C)C) of the Lagrangian density of a four (3 + 1)-dimensional QED by exploiting the horizontality condition defined on the six (4, 2)-dimensio...