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arXiv 1708.04461hep-th
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旋转粒子的世界片

World sheets of spinning particles

D. S. Kaparulin, S. L. Lyakhovich

备注：
references added, formulas in Section III.B included
发表信息：
Phys. Rev. D 96, 105014 (2017)
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摘要：

考虑了经典自旋粒子，使得经典模型的量子化导致庞加莱群的不可约质量表示。证明了在$d$维Minkowski空间中，规范等价经典粒子世界线类构成一个$[(d+1)/2]$维世界片，而与经典模型的任何细节无关.对于$d=3,4$中的大质量自旋粒子，世界片被证明是圆柱体。圆柱体的半径由表象确定。在更高的维度中，粒子的世界片是一个环形圆柱体$\mathbb{R}\times \mathbb{T}^D$，$D=[(d-1)/2]$。本文从不可约经典自旋粒子的世界线是圆柱曲线，而所有的世界线在同一世界片上都是规范等价的出发，提出了一种推导粒子经典运动方程和求其规范对称性的方法。在$d=3$ Minkowski空间中，自旋粒子路径由具有两个零阶规范对称性的单个四阶微分方程定义。该方程定义了粒子在闵可夫斯基空间中的运动轨迹，不涉及辅助变量。一个特殊的情况下，也被认为是圆柱形的零曲线，这是由一个不同的方程组定义。结果表明，圆柱形零曲线也对应于不可约的大质量自旋粒子。对于质量不可约的自旋粒子的高阶导数运动方程，我们导出了含有辅助变量的等价二阶形式。二阶公式与先前已知的自旋粒子模型一致。

英文摘要：

The classical spinning particles are considered such that quantization of classical model leads to an irreducible massive representation of the Poincaré group. The class of gauge equivalent classical particle world lines is shown to form a $[(d+1)/2]$-dimensional world sheet in $d$-dimensional Minkowski space, irrespectively to any specifics of classical model. For massive spinning particles in $d=3,4$, the world sheets are shown to be cylinders. The radius of cylinder is fixed by representation. In higher dimensions, particle's world sheet turn out to be a toroidal cylinder $\mathbb{R}\times \mathbb{T}^D$, $D=[(d-1)/2]$. Proceeding from the fact that the world lines of irreducible classical spinning particles are cylindrical curves, while all the lines are gauge equivalent on the same world sheet, we suggest a method to deduce the classical equations of motion for particles and also to find their gauge symmetries. In $d=3$ Minkowski space, the spinning particle path is defined by a single fourth-order differential equation having two zero-order gauge symmetries. The equation defines particle's path in Minkowski space, and it does not involve auxiliary variables. A special case is also considered of cylindric null-curves, which are defined by a different system of equations. It is shown that the cylindric null-curves also correspond to irreducible massive spinning particles. For the higher-derivative equation of motion of the irreducible massive spinning particle, we deduce the equivalent second-order formulation involving an auxiliary variable. The second-order formulation agrees with a previously known spinning particle model.

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