Geometrical Aspects Of BRST Cohomology In Augmented Superfield Formalism

TL;DR

This paper explores the geometrical foundations of BRST and co-BRST charges in gauge theories using augmented superfield formalism, illustrating their role in Hodge decomposition within 2D QED.

Contribution

It provides a geometric interpretation of BRST-related charges and demonstrates 2D QED as a unique model for Hodge theory in gauge field contexts.

Findings

Derived nilpotent symmetries for 2D QED fields.

Linked charges to de Rham cohomology operators.

Showed 2D QED as a tractable Hodge theory model.

Abstract

In the framework of augmented superfield approach, we provide the geometrical origin and interpretation for the nilpotent (anti-)BRST charges, (anti-)co-BRST charges and a non-nilpotent bosonic charge. Together, these local and conserved charges turn out to be responsible for a clear and cogent definition of the Hodge decomposition theorem in the quantum Hilbert space of states. The above charges owe their origin to the de Rham cohomological operators of differential geometry which are found to be at the heart of some of the key concepts associated with the interacting gauge theories. For our present review, we choose the two $(1 + 1)$-dimensional (2D) quantum electrodynamics (QED) as a prototype field theoretical model to derive all the nilpotent symmetries for all the fields present in this interacting gauge theory in the framework of augmented superfield formulation and show that this theory is a {\it unique} example of an interacting gauge theory which provides a tractable field theoretical model for the Hodge theory.