Geometrizing non-relativistic bilinear deformations

• Published in: The journal of high energy physics Vol. 2021; no. 4; pp. 1 - 42
• Main Authors: Hansen, Dennis, Jiang, Yunfeng, Xu, Jiuci
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2021; Springer Nature B.V; SpringerOpen
• Subjects: 2D Gravity; Classical and Quantum Gravitation; Deformation; Elementary Particles; Field Theories in Lower Dimensions; Field theory; High energy physics; Integrable Field Theories; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativistic effects; Relativistic theory; Relativity Theory; String Theory; Field Theories in Lower Dimensions; 2D Gravity; Integrable Field Theories
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP04(2021)186

A bstract We define three fundamental solvable bilinear deformations for any massive non-relativistic 2d quantum field theory (QFT). They include the T 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.