重参数化不变非相对论系统的超变量和BRST方法
Supervariable and BRST Approaches to a Reparameterization Invariant Non-Relativistic System
摘要：
我们利用超变量和Becchi-Rouet-Stora-Typhoon（BRST）形式主义的理论强度，导出了非相对论性（NR）自由粒子的重参数化不变模型的正确（即离壳幂零和绝对反对易）（反）BRST对称变换，该模型的空间$(x)$和时间$(t)$变量是演化参数$(τ)$的函数.我们的理论的无穷小重参数化（即一维同态）对称变换定义为w.r.t.这个演化参数$(τ)$。我们应用修改后的Bonora-Tonin（BT）超变方法（MBTSA）以及（反）手性超变方法（ACSA）BRST形式主义，讨论我们目前的系统的各个方面。为此，我们的1D普通理论（参数化$τ$）推广到$(1, 2)$维的超流形，其特征在于超空间坐标$Z^M = (τ, θ, \barθ)$，其中一对格拉斯曼变量满足费米子关系：$θ^2 = {\barθ}^2 = 0, \, θ\,\barθ+ \barθ\,θ= 0$和$τ$是玻色演化参数。在ACSA的上下文中，我们只考虑一般（1，2）维超流形的（1，1）维（反）手征超子流形。从各种潜在的理论方法中推导出普遍的Curci-Ferrari（CF）型限制，是我们目前努力的一个新观察。此外，我们注意到，规范固定和Faddeev-Popov鬼项的形式为我们的NR和非超对称系统是完全相同的重新参数化不变的超对称（即自旋）和非超对称（即标量）相对论粒子。这也是一个新奇的观察。
英文摘要：
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.
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