We analyze a particle constrained to move on a (p, q)-torus knot within the framework of supervariable approach and deduce the BRST as well as anti-BRST symmetries. We also capture the nilpotency and absolute anti-commutativity of (anti-)BRST symmetries in this framework. Further, we show the existence of some novel symmetries in the system such as (anti-)co-BRST, bosonic, and ghost scale symmetries. We demonstrate that the conserved charges (corresponding to these symmetries) adhere to an algebra which is analogous to that of de Rham cohomological operators of differential geometry. As the charges (and the symmetries) find a physical realization with the differential geometrical operators, at the algebraic level, the present model presents a prototype for Hodge theory.

我们在超变量方法的框架内分析了一个被约束在 ( p ,  q ) 环面结上移动的粒子，并推导出 BRST 以及反 BRST 对称性。我们还在这个框架中捕获了（反）BRST 对称性的幂零性和绝对反交换性。此外，我们还证明了系统中存在一些新颖的对称性，例如（反）共 BRST、玻色子和鬼尺度对称性。我们证明守恒电荷（对应于这些对称性）遵循一个类似于微分几何的 de Rham 上同调算子的代数。当电荷（和对称性）在代数层面上用微分几何算子找到物理实现时，本模型提出了霍奇理论的原型。