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We derive expressions for the charge and spin response function for theTomonaga model with quadratic dispersion and arbitrary (but finite for zeromomentum) interaction. For constant interaction these expressions are analyticand for other types of interaction only a simple matrix has to be diagonalised.We use a truncated expansion in particle-hole states with and without inclusionof correlations in the ground state yielding an exact result for pureintra-band interaction. We also discuss the possibility of power-laws in thedynamic structure factor for the spinful and spinless model.

Charge and spin response functions for the Tomonaga model with quadratic dispersion and different interactions