We derive on-shell recursion relations for nonrelativistic effective field theories (EFTs) with enhanced soft limits. The recursion relations are illustrated through analytic calculation of tree-level scattering amplitudes in theories with a complex Schrödinger-type field, real scalar with linear dispersion relation, and real scalar with Lifshitz-type dispersion relation. Our results show that the landscape of gapless nonrelativistic EFTs with local S-matrix can be constrained by soft theorems and the consistency of the low-energy S-matrix similarly to massless relativistic EFTs.

中文翻译：

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非相对论有效场论的壳上递归关系

我们推导出具有增强软限制的非相对论有效场论 (EFT) 的壳上递归关系。通过对复杂薛定谔型场、具有线性色散关系的实标量和具有Lifshitz型色散关系的实标量的理论中树级散射幅度的解析计算来说明递归关系。我们的结果表明，与无质量相对论 EFT 类似，具有局部S矩阵的无间隙非相对论 EFT 的景观可以受到软定理和低能量S矩阵的一致性的约束。