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We consider zero temperature behavior of dynamic response functions of 1Dsystems near edges of support in momentum-energy plane $(k, \omega).$ Thedescription of the singularities of dynamic response functions near an edge$\epsilon(k)$ is given by the effective Hamiltonian of a mobile impurity movingin a Luttinger liquid. For Galilean-invariant systems, we relate the parametersof such an effective Hamiltonian to the properties of the function $\epsilon(k).$ This allows us to express the exponents which characterize singularresponse functions of spinless bosonic or fermionic liquids in terms of$\epsilon(k)$ and Luttinger liquid parameters for any $k.$ For anantiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2)invariance fixes the exponents from purely phenomenological considerations.

Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit