Abstract
We exploit the standard techniques of the supervariable approach to derive the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a toy model of the Hodge theory (i.e., a rigid rotor) and provide the geometrical meaning and interpretation to them. Furthermore, wealsoderive the nilpotent (anti-)co-BRST symmetry transformations for this theory within the framework of the above supervariable approach. We capture the (anti-)BRST and (anti-)co-BRST invariance of the Lagrangian of our present theory within the framework of augmented supervariable formalism. We also express the (anti-)BRST and (anti-)co-BRST charges in terms of the supervariables (obtained after the application of the (dual-)horizontality conditions and (anti-)BRST and (anti-)co-BRST invariant restrictions) to provide the geometrical interpretations for their nilpotency and anticommutativity properties. The application of the dual-horizontality condition and ensuing proper (i.e., nilpotent and absolutely anticommuting) fermionic (anti-)co-BRST symmetries are completelynovelresults in our present investigation.
Highlights
The model of a rigid rotor has played a very decisive role in unraveling some of the deepest mysteries of nature
Advances in High Energy Physics for theco-BRST symmetry transformations within the framework of superfield approach to BRST formalism [5,6,7,8]. We resolve this issue in our present investigation by applying the augmented version of dual-horizontality condition (DHC) and derive the proper nilpotentcoBRST symmetry transformations and provide the geometrical basis for their existence in the same manner as that of theBRST symmetries
We have provided the geometrical basis for the nilpotency and absolute anticommutativity of theco-BRST charges (on the same lines as we have provided for theBRST charges in our earlier work [4])
Summary
The model of a rigid rotor has played a very decisive role in unraveling some of the deepest mysteries of nature (especially in the context of atomic, molecular, and nuclear physics). Advances in High Energy Physics for the (anti-)co-BRST symmetry transformations within the framework of superfield approach to BRST formalism [5,6,7,8] We resolve this issue in our present investigation by applying the augmented version of dual-horizontality condition (DHC) and derive the proper nilpotent (anti-)coBRST symmetry transformations and provide the geometrical basis for their existence in the same manner as that of the (anti-)BRST symmetries (which has already been done in our earlier work [4]). In our Appendix, we perform an explicit computation which is used in the main body of our text in the context of application of the dual-horizontality condition (DHC)
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