非相对论有效场论中的系统算符构造：希尔伯特系列与杨张量
Systematic Operator Construction for Non-relativistic Effective Field Theories: Hilbert Series versus Young Tensor
AI总结：
本文提出非相对论有效场论中算符构造的系统框架，利用希尔伯特系列和杨张量方法，构建了重粒子、介子-less有效理论及暗物质-核子相互作用的算符基。
摘要：
本文建立了一个非相对论有效场论中算符构造的系统框架，结合三维欧几里得对称性和内部对称性。通过采用旋转群的双覆盖，我们将希尔伯特系列扩展到非相对论系统，并消除了由自旋算符引入的冗余。我们还通过SU(2)半标准杨表将杨张量方法推广到非相对论情况，这允许在任意给定的质量维下构造具有重复场的算符基。利用杨张量技术和希尔伯特系列作为交叉验证，我们获得了以下情况的完整算符基：重粒子（及重夸克）有效理论算符到质量维9；不考虑介子的有效理论算符，包括核子-核子接触相互作用到O(Q^4)和三核子相互作用到O(Q^2)；以及最后自旋-1/2暗物质-核子算符到O(v^4)。
英文摘要：
This work establishes a systematic framework for operator construction in the non-relativistic effective field theory, incorporating both the three dimensional Euclidean symmetry and the internal symmetries. By employing double cover of the rotation group, we extend the Hilbert series to the non-relativistic systems, and eliminates redundancies introduced by the spin operator. We also generalize the Young tensor method to the non-relativistic cases through the $SU(2)$ semi-standard Young tableaux, which allows for the construction of operator bases with repeated fields at any given mass dimension. Utilizing the Young tensor technique and Hibert series as cross-check, we obtain the complete operator bases for the following cases: heavy particle (and also heavy quark) effective theory operators up to mass dimension 9; pion-less effective theory operators, including nucleon-nucleon contact interactions up to $\mathcal{O}(Q^4)$ and three-nucleon interactions at $\mathcal{O}(Q^2)$; and finally the spin-1/2 dark matter-nucleon operators up to $\mathcal{O}(v^4)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
