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We investigate local quantum field theories for one-dimensional (1D) Bose andFermi gases with contact interactions, which are closely connected with eachother by Girardeau's Bose-Fermi mapping. While the Lagrangian for bosonsincludes only a two-body interaction, a marginally relevant three-bodyinteraction term is found to be necessary for fermions. Because of thisthree-body coupling, the three-body contact characterizing a local triadcorrelation appears in the energy relation for fermions, which is one of thesum rules for a momentum distribution. In addition, we apply in both systemsthe operator product expansion to derive large-energy and momentum asymptoticsof a dynamic structure factor and a single-particle spectral density. Thesebehaviors are universal in the sense that they hold for any 1D scatteringlength at any temperature. The asymptotics for the Tonks-Girardeau gas, whichis a Bose gas with a hardcore repulsion, as well as the Bose-Fermicorrespondence in the presence of three-body attractions are also discussed.

Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions