Through the calculation of the effective potential and the excited state energies for the sinh-Gordon and the sine-Gordon models in dimensions, we show that the variational technique of Bogoliubov transformations is equivalent to the Gaussian wave-functional approach.
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.