ANALYSIS OF A NONLINEAR FOURTH ORDER DIFFERENTIAL EQUATION

An alternative approach to our earlier work regarding the canonical quantization of the phase space as a direct approach to the quantum statistical mechanics is presented. In this method, Feynmanʹs path integral technique of quantization in configuration space is extended to the phase space. This is done by introducing an extended lagrangian and an extended action as functions of phase space variables. As an illustration, the case of a harmonic potential is worked out explicitly.