Superfield approach to symmetry invariance in QED with complex scalar fields

TL;DR

This paper demonstrates that the Grassmannian independence of the super Lagrangian density on a (4, 2)-dimensional supermanifold provides a clear geometric proof of BRST and anti-BRST invariance in a 4D QED model with complex scalar fields.

Contribution

It introduces a superfield approach on a (4, 2)-dimensional supermanifold to geometrically prove BRST invariance in scalar QED.

Findings

Grassmannian independence implies BRST invariance

Superfield formalism encodes symmetry as translations along Grassmann directions

Geometric interpretation of gauge invariance in superfield language

Abstract

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 corresoponding 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 parametrized by the ordinary four spacetime variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of Grassmannian variables \theta 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.