The stochastic theory of subsurface solute transport has received stimulus recently from modeling techniques originating in quantum field theory (QFT), resulting in new calculations of the solute macrodispersion tensor that derive from the solving Dyson equation with a subsequent renormalization group analysis. In this paper, we offer a critical evaluation of these techniques as they relate specifically to the derivation of a field-scale advection-dispersion equation. An approximate Dyson equation satisfied by the ensemble-average solute concentration for tracer movement in a heterogeneous porous medium is derived and shown to be equivalent to a truncated cumulant expansion of the standard stochastic partial differential equation which describes the same phenomenon. The full Dyson equation formalism, although exact, is of no importance to the derivation of an improved field-scale advection-dispersion equation. Similarly, renormalization group analysis of the macrodispersion tensor has not yet provided results that go beyond what is available currently from the cumulant expansion approach.