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Geometrizing non-relativistic bilinear deformations. (English) Zbl 1462.81129

Summary: We define three fundamental solvable bilinear deformations for any massive non-relativistic 2d quantum field theory (QFT). They include the \(\text{T}\overline{\text{T}}\) deformation and the recently introduced hard rod deformation. We show that all three deformations can be interpreted as coupling the non-relativistic QFT to a specific Newton-Cartan geometry, similar to the Jackiw-Teitelboim-like gravity in the relativistic case. Using the gravity formulations, we derive closed-form deformed classical Lagrangians of the Schrödinger model with a generic potential. We also extend the dynamical change of coordinate interpretation to the non-relativistic case for all three deformations. The dynamical coordinates are then used to derive the deformed classical Lagrangians and deformed quantum S-matrices.

MSC:

81T10 Model quantum field theories
81U20 \(S\)-matrix theory, etc. in quantum theory
83C80 Analogues of general relativity in lower dimensions
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
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