Higher-order propagators primitive propagator

It is worth noting that within the PI implementation, we are mainly interested in evaluating the trace of the density matrix, as it is directly related to the partition function. Also when using the primitive approximation, we neglect terms that are of the order x. To improve the precision of results in MC simulations and to achieve faster convergence as P increases, higher order corrections (or propagators of the density matrix) have been developed. 

User-specified, temporal ordering of operational goals at higher levels of abstraction is propagated downwards in the hierarchy goals and is ultimately expressed as temporal ordering of primitive operations (see Section III,B). 

One direction in which improvements on the primitive propagator Eq. (19) can be found is to search for higher-order approximants, which allow one to obtain a given level of accuracy with a lower P. In this respect, an indispensable tool is the general Baker-Campbell-Hausdorff formula for two noncommutable operators A and B [66]... 

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