Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-03-23
Int.J.Geom.Meth.Mod.Phys.1:467-492,2004
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX file, 25 pages, Ref. [49] updated, correct page numbers of the Journal are given
Scientific paper
10.1142/S0219887804000241
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.
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