想念漫游 - 王贰浪

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.

Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one--dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of partial derivatives in the Schrödinger operator. Consequences for quantum cosmology are shortly discussed.