Theory of critical first sound near theλtransition ofHe4. I. Model and correlation functions

A detailed foundation and general discussion are given for a new model that describes the critical dynamics of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ near $T_{\lambda }$, including the thermal-diffusion and first-sound modes. All parameters are identified in terms of thermodynamic and hydrodynamic quantities. The relation between static and dynamic correlation functions of our model and those of the simpler model F is derived. This provides the basis for a quantitative theory of critical first sound.