Variational basis-state expansion calculation of the mass gap in scalar field theory

We use the variational basis-state expansion method to compute the fundamental particle mass for the scalar field theory :λ(${\phi }^6$-${\phi }^4$) +(1/2${\mu }^2$ ${\phi }^2$: in 1+1 dimensions. The variational ansatz is a linear superposition of the known states of the scalar field theory defined by ${\mathrm{scrL}}_0$=(1/2${\partial }_{\mu }$φ${\partial }^{\mu }$φ-1)/2 ${\Omega }^2$ ${\phi }^2$, where Ω is a variational parameter. Results for the mass gap $m_1$ are obtained, using a superposition of one- to nine-particle states of ${\mathrm{scrL}}_0$ as the variational trial states. Our results are compared to spatial-lattice calculations of the mass gap for this model.