论文标题
可超级和BRST的方法来重新聚集不变的非相关系统
Supervariable and BRST Approaches to a Reparameterization Invariant Non-Relativistic System
论文作者
论文摘要
我们利用可超级和贝奇 - 鲁贝 - 遗传蛋白质（BRST）形式主义的理论强度来得出适当的（即，偏离静止和绝对反态）（抗抗抗药性）（反 - ）BRST对称性转换，以使空间的非元素（$ nr）$（NR）$（NR）$（NR）$（NR）$（NR）$（x）的$（x）$（x）$（x）$（x）参数$（τ）$。 W.R.T.定义了无限的重新聚集（即1D差异）对称转换。此Evolution参数$（τ）$。我们将修改后的Bonora-Tonin（BT）可让您的方法（MBTSA）以及（反）手性监督方法（ACSA）用于讨论我们当前系统的各个方面。为此，我们的1D普通理论（由$τ$参数化）被推广到$（1，2）$ - 维度超人质量上，其特征是超空间坐标$ z^m =（τ，θ，θ，\barθ）$，其中一对格拉曼尼亚变量可满足纤维化关系： θ\，\barθ+ \barθ\，θ= 0 $，$τ$是骨传感参数。在ACSA的背景下，我们仅考虑（1，1） - 维（抗）手性超级子术的（1，2） - 维度超级曼物。在我们目前的努力中，来自各种基本理论方法的普遍姜黄（CF）型限制的推导是一种新颖的观察。此外，我们注意到，对于我们的NR和非吸烟系统的量规和Faddeev-Popov幽灵术语的形式与重新聚集不变的Susy（即旋转）和非舒适（即标量表）相对论粒子完全相同。这也是一个新颖的观察。
We exploit the theoretical strength of the supervariable and Becchi-Rouet-Stora-Tyutin (BRST) formalisms to derive the proper (i.e. off-shell nilpotent and absolutely anticommuting) (anti-)BRST symmetry transformations for the reparameterization invariant model of a non-relativistic (NR) free particle whose space $(x)$ and time $(t)$ variables are function of an evolution parameter $(τ)$. The infinitesimal reparameterization (i.e. 1D diffeomorphism) symmetry transformation of our theory is defined w.r.t. this evolution parameter $(τ)$. We apply the modified Bonora-Tonin (BT) supervariable approach (MBTSA) as well as the (anti-)chiral supervariable approach (ACSA) to BRST formalism to discuss various aspects of our present system. For this purpose, our 1D ordinary theory (parameterized by $τ$) is generalized onto a $(1, 2)$-dimensional supermanifold which is characterized by the superspace coordinates $Z^M = (τ, θ, \barθ)$ where a pair of Grassmannian variables satisfy the fermionic relationships: $θ^2 = {\barθ}^2 = 0, \, θ\,\barθ+ \barθ\,θ= 0$ and $τ$ is the bosonic evolution parameter. In the context of ACSA, we take into account only the (1, 1)-dimensional (anti-)chiral super sub-manifolds of the general (1, 2)-dimensional supermanifold. The derivation of the universal Curci-Ferrari (CF)-type restriction, from various underlying theoretical methods, is a novel observation in our present endeavor. Furthermore, we note that the form of the gauge-fixing and Faddeev-Popov ghost terms for our NR and non-SUSY system is exactly same as that of the reparameterization invariant SUSY (i.e. spinning) and non-SUSY (i.e. scalar) relativistic particles. This is a novel observation, too.
