Note on the nonrelativistic $T\bar{T}$ deformation

TL;DR

This paper investigates the nonrelativistic $Tar{T}$ deformation of complex scalar field theory, deriving the deformed Lagrangian and exact energy spectrum using perturbative and analytical methods.

Contribution

It provides the first explicit form of the deformed Lagrangian and exact energy spectrum for nonrelativistic $Tar{T}$-deformed theories.

Findings

Derived the closed-form deformed Lagrangian.

Computed the exact energy spectrum of the deformed free theory.

Used perturbation and characteristic methods for analysis.

Abstract

In this paper, we present our study on the $T\bar{T}$-deformation of non-relativistic complex scalar field theory. We find the closed form of the deformed Lagrangian by using the perturbation and the method of characteristics. Furthermore we compute the exact energy spectrum of the deformed free theory by using the Brillouin-Wigner perturbation theory in an appropriate regularization scheme.