  We have recently employed periodic Anderson model with electron-phonon
interactions to describe Cerium volume collapse ($\gamma \rightarrow \alpha$
transition) under pressure. To describe the volume collapse transition in
Cerium, we have tried to plot the pressure versus volume curves and see when a
kink structure emerges. One way to obtain the pressure versus volume curve is
to calculate the total energy of the system at different temperatures. In order
to solve the periodic Anderson model with electron-phonon interactions, we have
used the continuous time quantum Monte Carlo algorithm by integrating out the
phonons to obtain a retarded electron-electron interaction. Monte Carlo
simulation results give us the model's electronic Green function and self
energy, from which we can calculate the system's total energy. A well known
formula for calculating total energy through the knowledge of electron's self
energy and Green function is derived from the model's Hamiltonian, which is not
available for our case. Here, we have devised a new method to derive the total
energy formula purely from a path integral description of the system, without
resort to its Hamiltonian formulation. Since not all systems can be described
by a Hamiltonian, thus our method has a wider applicability. It is noteworthy
that the total energy formula that we derived here takes an identical form with
that obtained from a model's Hamiltonian.
