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arXiv · 2012.12290

Geometrizing non-relativistic bilinear deformations

Dennis Hansen·Yunfeng Jiang·Jiuci Xu
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Abstract

We define three fundamental solvable bilinear deformations for any massive non-relativistic 2d quantum field theory (QFT). They include the $\mathrm{T}\overline{\mathrm{T}}$ 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 Schr\"odinger 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.

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Dennis Hansen, Yunfeng Jiang, Jiuci Xu. 2020-12-22. Geometrizing non-relativistic bilinear deformations. https://doi.org/10.1007/jhep04(2021)186

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