On-Shell Recursion Relations for Nonrelativistic Effective Field Theories

Abstract

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.

7 pages; v2: matches version published in PLB plus an additional reference

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• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
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Cited by in corpus (7)

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• Soft Phonon Theorems
• Fractional soft limits