Abstract
The path integral method of quantum mechanics introduced by Feynman is used to derive the recently developed selfconsistent theory of anharmonic lattice dynamics. The method allows a simple and rigorous derivation of the theory to all orders. The simplicity is obtained from integral representation of the partition function while the rigour is obtained from use of a general extremum principle rather than reliance on a variational principle. The first and second orders are derived explicitly including a derivation of the phonon frequencies via the method in each order. Close comparisons are made with the previous derivations by Choquard, Horner and Werthamer and the Green function expansion, which underline the differences in method and result.