2005/10/31 by R. P. Malik · 1 citation
Mathematics · Physics and Astronomy · #BRST quantization #Black Holes and Theoretical Physics #Covariant transformation #Gauge theory #Geometry #Grassmannian #Homogeneous space #Mathematical physics #Mathematics #Nilpotent #Noncommutative and Quantum Gravity Theories #Nonlinear Waves and Solitons #Physics #Pure mathematics #Supermanifold #Superspace #Supersymmetric gauge theory #Supersymmetry #hep-th
paper · pdf · doi:10.1088/0305-4470/39/33/023
published as J.Phys.A39:10575-10587,2006 · LaTeX file, 15 pages, journal-version
openalex publication_date 2006/08/02 · arxiv created 2006/08/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 ( A μ ), the (anti-)ghost fields and the Dirac fields 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 even spacetime coordinates x μ (μ = 0, 1, 2, 3) and two odd Grassmannian variables θ and parametrize this six-dimensional supermanifold. The new gauge invariant restriction on the above supermanifold owes its origin to the (super) covariant derivatives and their intimate relations with the (super) 2-form curvatures constructed with the help of 1-form (super)gauge connections and (super) exterior derivatives . The results obtained by exploiting (i) the horizontality condition, and (ii) one of its consistent extensions, are shown to be a simple consequence of this new single restriction on the above supermanifold. Thus, our present endeavour provides an alternative to (and, in some sense, generalization of) the horizontality condition of the usual superfield formalism applied to the derivation of BRST symmetries.