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.
Highlights
Solvable irrelevant deformations have attracted many interests in recent years due to their novel features that provide analytical control on the ultraviolet (UV) physics regardless of the difficulties from strong coupling or nonlocality
We find the closed form of the deformed Lagrangian by using the perturbation and the method of characteristics
We expect that the spectrum of (57) can be derived by performing the second quantization and applying the standard quantum perturbation theory
Summary
Solvable irrelevant deformations have attracted many interests in recent years due to their novel features that provide analytical control on the ultraviolet (UV) physics regardless of the difficulties from strong coupling or nonlocality. The standard integrability technique of solving these integrable deformed models is first to compute the deformed S matrix in the infinite volume limit where the deformation modifies the S matrix by multiplying a Castillejo-DalitzDyson factor [3,36,37], and to substitute the deformed S matrix into the Bethe equation to solve the theory in the finite volume Using this integrability technique, the deformed one-dimensional Bose gas known as the Lieb-Liniger model was carefully studied in [34] where the author showed that the deformed one-dimensional Bose gas shares many qualitative features with the TT -deformed relativistic quantum field theories. Our method in this work is similar to the one used in [40], and is somewhat complementary to the ones in2 [38,39]
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