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

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

1997-10-22

arxiv.org/abs/hep-th/9710173v1

Phys.Rev. D57 (1998) 5092-5099

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1103/PhysRevD.57.5092

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

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