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Applying the linear δ expansion to the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>i</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>interaction
The linear \ensuremath{\delta} expansion (LDE) is applied to the Hamiltonian $H=\frac{1}{2}{(p}^{2}{+m}^{2}{x}^{2}{)+igx}^{3},$ which arises in the study of Lee-Yang zeros in statistical mechanics. Despite being non-Hermitian, this Hamiltonian appears to possess a real, positive spectrum. In the LDE, as in perturbation theory, the eigenvalues are naturally real, so a proof of …