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arXiv · 1806.01898

Classical Nonrelativistic Effective Field Theories for a Real Scalar Field

Eric Braaten·Abhishek Mohapatra·Hong Zhang
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Abstract

A classical nonrelativistic effective field theory for a real Lorentz-scalar field $ϕ$ 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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Eric Braaten, Abhishek Mohapatra, Hong Zhang. 2018-06-05. Classical Nonrelativistic Effective Field Theories for a Real Scalar Field. https://doi.org/10.1103/physrevd.98.096012

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