刚性转子作为Hodge理论的玩具模型
Rigid Rotor as a Toy Model for Hodge Theory
摘要：
我们应用超场方法的玩具模型的刚性转子，并显示存在幂零和绝对anticommuting Becchi-Rouet-Stora-Tyrit（BRST）和反BRST对称变换，在此情况下，动力学项和行动保持不变。此外，我们还导出了离壳幂零和绝对反对易（反）co-BRST对称变换，在此变换下，规范固定项和拉格朗日量保持不变。上述幂零对称变换的反交换子导致了一个玻色对称变换的推导，在该变换下，鬼项和作用量保持不变。总之，上述变换（及其相应的生成元）所涉及的代数是微分几何中de Rham上同调算子所遵循的代数的物理实现。因此，我们现在的模型是霍奇理论的玩具模型。
英文摘要：
We apply the superfield approach to the toy model of a rigid rotor and show the existence of the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations, under which, the kinetic term and action remain invariant. Furthermore, we also derive the off-shell nilpotent and absolutely anticommuting (anti-) co-BRST symmetry transformations, under which, the gauge-fixing term and Lagrangian remain invariant. The anticommutator of the above nilpotent symmetry transformations leads to the derivation of a bosonic symmetry transformation, under which, the ghost terms and action remain invariant. Together, the above transformations (and their corresponding generators) respect an algebra that turns out to be a physical realization of the algebra obeyed by the de Rham cohomological operators of differential geometry. Thus, our present model is a toy model for the Hodge theory.
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