Nilpotent Symmetries for QED in Superfield Formalism

TL;DR

This paper derives nilpotent (anti-)BRST and (anti-)co-BRST symmetries for 2D QED using superfield approach, resolving longstanding issues in deriving matter field transformations via new supermanifold restrictions.

Contribution

It introduces novel restrictions on the supermanifold based on conserved current invariance, enabling the derivation of matter field symmetries in superfield formalism.

Findings

Derived nilpotent symmetry transformations for gauge and ghost fields.

Resolved the problem of deriving matter field symmetries in superfield approach.

Provided a geometric interpretation of the symmetries.

Abstract

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 $(A_\mu)$ and the (anti-)ghost fields $((\bar C)C)$ 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-standing problem of the derivation of the above symmetry transformations for the matter (Dirac) fields $(\bar\psi, \psi)$ in the framework of superfield formulation is resolved by a new set of restrictions on the $(2 + 2)$-dimensional supermanifold. These new physically interesting restrictions on the supermanifold owe their origin to the invariance of conserved currents of the theory. The geometrical interpretation for all the above transformations is provided in the framework of superfield formalism.