Bethe ansatz methods are used to obtain an exact expression for the energy density for a system consisting of the (1+1)-dimensional sine-Gordon model coupled to an external scalar source. This method exploits the equivalence between the sine-Gordon model and the massive Thirring model. These calculations allow one to test various loop-expansion approximations to the effective potential for the scalar. Such calculations are of relevance to fundamental issues regarding quantum hadrodynamics.

• Received 13 November 1989

DOI:https://doi.org/10.1103/PhysRevC.42.970