GAUSSIAN EFFECTIVE POTENTIAL ANALYSIS OF SINH(SINE)–GORDON MODELS NEW REGULARIZATION–RENORMALIZATION SCHEME

Using the new regularization and renormalization scheme recently proposed by Yang and used by Ni et al., we analyze the sine–Gordon and sinh–Gordon models within the framework of Gaussian effective potential in D+1 dimensions. Our analysis suffers no divergence and so does not suffer from the manipulational obscurities in the conventional analysis of divergent integrals. Our main conclusions agree exactly with those of Ingermanson for D=1,2 but disagree for D=3: the D=3 sinh(sine)–Gordon model is nontrivial. Furthermore, our analysis shows that for D=1,2, the running coupling constant (RCC) has poles for sine–Gordon model (γ2<0) and the sinh–Gordon model (γ2>0) has a possible critical point [Formula: see text] while for D=3, the RCC has poles for both γ2>0 and γ2<0.