A classical nonrelativistic effective field theory for a real Lorentz-scalar field ? is most conveniently formulated in terms of a complex scalar field ψ . There have been two derivations of effective Lagrangians for the complex field ψ in which terms in the effective potential were determined to order ( ψ * ψ ) 4 . We point out an error in each of the effective Lagrangians. After correcting the errors, we demonstrate the equivalence of the two effective Lagrangians by verifying that they both reproduce T -matrix elements of the relativistic real scalar field theory and by also constructing a redefinition of the complex field ψ that transforms terms in one effective Lagrangian into the corresponding terms of the other.
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