IMPROVED EFFECTIVE POTENTIAL BY NONLINEAR CANONICAL-TRANSFORMATIONS

We generalize the familiar gaussian-effective-potential formalism to a class of non-gaussian trial states. With the help of exact nonlinear canonical transformations, expectation values can be calculated analytically and in closed form. A detailed description of our method, particularly for quadratic and cubic transformatiions, and of the related renormalization procedure is given. Applications to Φ4-models in various dimensionalities are treated. We find the expected critical behaviour in two space-time dimensions. In three and four dimensions we observe instabilities which go back to the incompleteness of the gaussian-based renormalization. In the appendices it is shown that the quadratic transformation leads to a coherent state in a certain limiting case, and the generalization to systems at finite temperature is performed. © 1990 Springer-Verlag.