Abstract
Within the framework of augmented version of superfield formalism, we derive the superspace unitary operator and show its usefulness in the derivation of Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a set of interesting models for the Abelian 1-form gauge theories. These models are (i) a one (0+1)-dimensional (1D) toy model of a rigid rotor, (ii) the two (1+1)-dimensional (2D) modified versions of the Proca and anomalous Abelian 1-form gauge theories, and (iii) the 2D self-dual bosonic gauge field theory. We provide, in some sense, the alternatives to the horizontality condition (HC) and the gauge invariant restrictions (GIRs) in the language of the above superspace (SUSP) unitary operator. One of the key observations of our present endeavor is the result that the SUSP unitary operator and its Hermitian conjugate are found to be thesameforallthe Abelian models under consideration (including the 4DinteractingAbelian 1-form gauge theories with Dirac and complex scalar fields which have been discussed earlier). Thus, we establish theuniversalityof the SUSP operator for the above Abelian theories.
Highlights
The usual superfield approach [1,2,3,4,5,6,7,8] to Becchi-Rouet-StoraTyutin (BRST) formalism is a geometrically rich and physically very intuitive method which sheds light on the physical interpretation of the nilpotency and absolute anticommutativity property of the properBRST symmetries
The above superfield approach has been consistently generalized so as to derive theBRST symmetries for the gauge, associatedghost and matter fields of a given interactingAbelian 1-form gauge theory by invoking the horizontality condition (HC) and the gauge (i.e.,BRST) invariant restrictions (GIRs) on the superfields defined on the (D, 2)-dimensional supermanifold corresponding to a given D-dimensional interactingAbelian 1-form gauge theory defined on the D-dimensional flat Minkowski spacetime ordinary manifold
We have shown that the mathematical form of the SUSP unitary operator and its Hermitian conjugate is universal for the 1D, 2D, and 4D 1form gauge theories
Summary
The usual superfield approach [1,2,3,4,5,6,7,8] to Becchi-Rouet-StoraTyutin (BRST) formalism is a geometrically rich and physically very intuitive method which sheds light on the physical interpretation of the nilpotency and absolute anticommutativity property of the proper (anti-)BRST symmetries. We have applied the augmented version of superfield/supervariable formalism to derive the (anti-)BRST symmetries for the 2D and 1D Abelian 1-form gauge theories and expressed these results in terms of the SUSP unitary operators. It should be pointed out that all the gauge (i.e., (anti-)BRST) invariant quantities are required to be independent of the Grassmannian variables when they are generalized onto the appropriately chosen supermanifold This statement implies the following equality under the basic tenets of the augmented version of superfield formalism (see, e.g., [11,12,13,14]): λ((1h)) + dPr (t, θ, θ) = λ(1) (t) + dpr (t) , d = dt∂t, (16). A close and careful look at (22) and (31) demonstrates that we have obtained all the (anti-)BRST transformations for all the fields of the 2D modified version of the anomalous gauge theory
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