讴歌 - Vansdaddy

Schwinger's mechanism for mass generation relies on topological structures of a 2-dimensional gauge theory. In the same manner, corresponding 4-dimensional topological entities give rise to topological mass generation in four dimensions.

We prove that for non-linear L = L(R), the Lagrangians L and \hat L give conformally equivalent fourth-order field equations being dual to each other. The proof represents a new application of the fact that the operator

The solutions of two-dimensional gravity following from a non-linear Lagrangian L = f(R) are classified, and their symmetry and singularity properties are described. Then a conformal transformation is applied to rewrite these solutions as analogous solutions of two-dimensional Einstein-dilaton gravity and vice versa.