APPLYING THE LINEAR DELTA-EXPANSION TO THE I-PHI(3) INTERACTION

The linear delta expansion (LDE) is applied to the Hamiltonian H = 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. Tn the LDE, as in pertur bation theory, the eigenvalues are naturally real, so a proof of this property devolves on the convergence of the expansion. A proof of conv ergence of a modified version of the LDE is provided for the ix(3) pot ential in zero dimensions. The methods developed in zero dimensions ar e then extended to quantum mechanics, when we provide numerical eviden ce for convergence.