粒子的洛伦兹和排列不变量
Lorentz and permutation invariants of particles I
摘要：
Weyl的一个定理告诉我们，$n$粒子动量中的洛伦兹（和宇称）不变多项式是由点积产生的。考虑到量子场论中粒子是不可区分的这一事实，我们将这个结果推广到任意置换群$P \subset S_n$对粒子的作用。这样做提供了一组方便的变量来描述散射过程涉及相同的粒子，如$pp \to jjj$，我们提供了一个明确的洛伦兹和置换不变的发电机。
英文摘要：
A theorem of Weyl tells us that the Lorentz (and parity) invariant polynomials in the momenta of $n$ particles are generated by the dot products. We extend this result to include the action of an arbitrary permutation group $P \subset S_n$ on the particles, to take account of the quantum-field-theoretic fact that particles can be indistinguishable. Doing so provides a convenient set of variables for describing scattering processes involving identical particles, such as $pp \to jjj$, for which we provide an explicit set of Lorentz and permutation invariant generators.
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