Search

In this paper, we develop Schiff's discretization procedure for calculating the phase shifts in the $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ model in ($D+1$)-dimensional space-time ($Dg0$) with the Gaussian wave-functional approach. In 1+1 and 2+1 dimensions, the phase shifts are negative, which indicates the interaction between two pions is repulsive. In 3+1 dimensions, the phase shifts vanish. We also discuss the dependences of the phase shifts upon the scattering energy in detail.

The (1+1)-dimensional sine-Gordon model is studied in the framework of the variational Gaussian wave functionals. The renormalized mass depends on two dimensionless parameters. In the phase diagram a first-order phase transition will replace the second-order phase transition for large bare mass. The spectrum of the two-particle states consists of a continuum of scattering states and the isolated values connected to the excitonlike bound states. The energy of the bound states and the phase shifts of the scattering states are explicitly calculated.

A Rayleigh-Schr\"odinger perturbation theory based on the Gaussian wave functional is constructed. The method can be used for calculating the energies of both the vacuum and the excited states. A model calculation is carried out for the vacuum state of the $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ field theory.