Discretized path-integral quantum dynamics

By comparing analogous terms in ( , x) and Q, we see that we can think of the partition function as a path integral over periodic orbits that recur in a complex time interval equal to i s flh/i = — ifih. There is no claim here that the closed paths used to generate Q correspond to actual quantum dynamics, but simply that there is an isomorphism. We therefore can refer to the equation above as the discretized path-integral (DPI) representation of the partition function. Using Feynman s notation, we have in the infinite-P limit... 

We shall be concerned with the computation of real-time quantities (e.g., correlation functions or time-dependent occupation probabilities). The standard approach in a QMC simulation of such dynamical quantities consists of constructing a suitably discretized path integral expression for the quantum mechanical propagator of the system... 

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