Hodge理论玩具模型幂零对称性的超变量方法
Supervariable Approach to the Nilpotent Symmetries for a Toy Model of the Hodge Theory
摘要：
我们利用超变量方法的标准技术，推导出幂零的Becchi-Rouet-Stora-Tyrons（BRST）和反BRST对称变换的霍奇理论的玩具模型（即刚性转子），并提供几何意义和解释。此外，我们还推导出幂零（反）co-BRST对称变换的框架内，上述超变量的方法。我们捕获的（反）BRST和（反）合作BRST不变性的拉格朗日我们目前的理论框架内的增广超变量形式主义。我们还表示的（反）BRST和（反）co-BRST收费的超变量（后获得的应用程序的（双）水平性条件和（反）BRST和（反）co-BRST不变的限制），以提供其幂零性和反交换性的几何解释。双水平性条件的应用和随之而来的适当的（即幂零和绝对反交换）费米子（反）co-BRST对称性是完全新的结果，在我们目前的调查。
英文摘要：
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, we also derive 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 completely novel results in our present investigation.
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