Applying the linear delta expansion to `i phi^3'

Abstract

The linear $\delta$ expansion (LDE) is applied to the Hamiltonian $H=(p^2+m^2{x}^2)/2+ig{x}^3$, 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 this property devolves on the convergence of the expansion. A proof of convergence of a modified version of the LDE is provided for the $i{x}^3$ potential in zero dimensions. The methods developed in zero dimensions are then extended to quantum mechanics, where we provide numerical evidence for convergence.

26 pages (revtex), 8 figures (eps). Submitted to Phys. Rev. D

References in corpus (1)

• Applying the linear δ-expansion to disordered systems

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