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A classical nonrelativistic effective field theory for a real Lorentz-scalarfield $\phi$ is most conveniently formulated in terms of a complex scalar field$\psi$. There have been two derivations of effective Lagrangians for thecomplex field $\psi$ in which terms in the effective potential were determinedto order $(\psi^* \psi)^4$. We point out an error in each of the effectiveLagrangians. After correcting the errors, we demonstrate the equivalence of thetwo effective Lagrangians by verifying that they both reproduce $T$-matrixelements of the relativistic real scalar field theory and by also constructinga redefinition of the complex field $\psi$ that transforms terms in oneeffective Lagrangian into the corresponding terms of the other.

Classical Nonrelativistic Effective Field Theories for a Real Scalar Field