B P Mandal
Articles written in Pramana – Journal of Physics
Volume 72 Issue 3 March 2009 pp 505-515 Research Articles
Nilpotent symmetry invariance in the non-Abelian 1-form gauge theory: Superfield formalism
We demonstrate that the nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four $(3 + 1)$-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the frame-work of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field and the Dirac fields, is considered on a (4,2)-dimensional supermanifold, parametrized by the bosonic 4D space-time variables and a pair of Grassmannian variables. We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the (4,2)-dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original 4D theory.
Volume 72 Issue 5 May 2009 pp 805-818 Research Articles
Superfield approach to symmetry invariance in quantum electrodynamics with complex scalar fields
We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the superfields defined on a $(4,2)$-dimensional supermanifold, is a clear-cut proof for the Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST invariance of the corresponding four $(3+1)$-dimensional (4D) Lagrangian density that describes the interaction between the $U(1)$ gauge field and the charged complex scalar fields. The above 4D field theoretical model is considered on a $(4,2)$-dimensional supermanifold para- metrized by the ordinary four space-time variables $x^{\mu}$ (with $\mu = 0, 1, 2, 3$) and a pair of Grassmannian variables 𝜃 and $\bar{\theta}$ (with $\theta^{2} = \bar{\theta}^{2} = 0$, $\theta\bar{\theta} + \bar{\theta}\theta = 0$). Geometrically, the (anti-)BRST invariance is encoded in the translation of the super-Lagrangian density along the Grassmannian directions of the above supermanifold such that the outcome of this shift operation is zero.
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