Effective field theory for one-dimensional nonrelativistic particles with contact interaction
arXiv:1711.10517 · doi:10.1103/PhysRevA.97.043630
Abstract
We consider a field theory describing interacting nonrelativistic particles of two types, which map to each other under time reversal, with point-like interaction. We identify a new type of interaction which depends on the relative velocity between the particles. We compute the renormalization group running of the coupling constants and find a fixed point and a fixed line. We show that the scattering amplitudes can be expressed in terms of three parameters. The result matches with a quantum mechanical analysis and represents the most general point-like interaction consistent with unitarity and time reversal invariance.
arXiv comment11 pages, 2 figures
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