Geometrical Aspects Of BRST Cohomology In Augmented Superfield Formalism

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.

LaTeX file, 25 pages, Ref. [49] updated, correct page numbers of the Journal are given

References in corpus (5)

• Superfield Approach to Symmetries for Matter Fields in Abelian Gauge Theories
• Abelian 2-form gauge theory: special features
• Nilpotent Symmetries for QED in Superfield Formalism
• Superfield Approach to (Non-)local Symmetries for One-Form Abelian Gauge Theory
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Cited by in corpus (12)

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• Unique Nilpotent Symmetry Transformations For Matter Fields In QED: Augmented Superfield Formalism
• Superfield Approach To Nilpotent Symmetries For QED From A Single Restriction: An Alternative To The Horizontality Condition
• Nilpotent Symmetries For A Spinning Relativistic Particle In Augmented Superfield Formalism
• Augmented Superfield Approach To Unique Nilpotent Symmetries For Complex Scalar Fields In QED
• A Generalization Of The Horizontality Condition In The Superfield Approach To Nilpotent Symmetries For QED With Complex Scalar Fields
• Augmented Superfield Approach To Exact Nilpotent Symmetries For Matter Fields In Non-Abelian Theory
• Hodge Duality Operation And Its Physical Applications On Supermanifolds
• Augmented Superfield Approach to Gauge-invariant Massive 2-Form Theory
• Nilpotent symmetry invariance in the superfield formulation: the (non-)Abelian 1-form gauge theories
• Nilpotent symmetry invariance in the non-Abelian 1-form gauge theory: superfield formalism
• Superfield approach to symmetry invariance in QED with complex scalar fields