论文标题

为所有质量和旋转构建通用的有效现场理论

Constructing Generic Effective Field Theory for All Masses and Spins

论文作者

Dong, Zi-Yu, Ma, Teng, Shu, Jing, Zheng, Yu-Hui

论文摘要

我们充分解决了具有任何质量和旋转的田野的运营商基础构造问题。基于壳的方法,我们提出了一种新颖的方法,可以通过在任何给定的维度上系统地构建一组完整的尺寸幅度底座,该尺寸通过Lorentz Subgroup $ su(2)_r $和全球对称性$ u(n)$($ n $)($ n是外部腿的数量)的半标准的年轻tableaus,可以直接映射到物理经验家底部。我们首先构造了一组完整的单基底座,其尺寸不是最低和一组冗余的碱基集,这些底座始终包含一组完整的振幅碱基,这些幅度最低。然后,我们将冗余设置的基础分解为从低尺寸到高尺寸的单元碱基,并消除线性相关碱基。最后,可以捡起最低维度的基础。我们还提出了一种矩阵投影方法,以构建涉及相同颗粒的大量振幅碱基。通用大规模有效的现场理论的操作员群可以由计算机程序有效地构建。提出了最多六个尺寸的一组四矢量运算符。

We fully solve the long-standing problem of operator basis construction for fields with any masses and spins. Based on the on-shell method, we propose a novel method to systematically construct a complete set of lowest dimensional amplitude bases at any given dimension through semi-standard Young tableaus of Lorentz subgroup $SU(2)_r$ and global symmetry $U(N)$ ($N$ is the number of external legs), which can be directly mapped into physical operator bases. We first construct a complete set of monomial bases whose dimension is not the lowest and a redundant set of bases that always contains a complete set of amplitude bases with the lowest dimension. Then we decompose the bases of the redundant set into the monomial bases from low to high dimension and eliminate the linear correlation bases. Finally, the bases with the lowest dimension can be picked up. We also propose a matrix projection method to construct the massive amplitude bases involving identical particles. The operator bases of a generic massive effective field theory can be efficiently constructed by the computer programs. A complete set of four-vector operators at dimensions up to six is presented.

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