We present a second order gravity action which consists of ordinary Einstein action augmented by a first-order, vector like, Chern-Simons quasi topological term. This theory is ghost-free and propagates a pure spin-2 mode. It is diffeomorphism invariant, although its local Lorentz invariance has been spontaneuosly broken.

We use the group of Abelian surfaces to develop a gauge-independent quantization for the two-index antisymmetric potential. An exact solution is found for the vacuum and the photon state, and a regularization scheme is proposed.

It is shown that the Topological Massive and "Self-dual" theories, which are known to provide locally equivalent descriptions of spin 1 theories in 2+1 dimensions, have different global properties when formulated over topologically non-trivial regions of space-time. The partition function of these theories, when constructed on an arbitrary Riemannian manifold, differ by a topological factor, which is equal to the partition function of the pure Chern-Simons theory. This factor is related to the space of solutions of the field equations of the Topological Massive Theory for which the connection is asymptotically flat but not gauge equivalent to zero. A new covariant, first order, gauge action,which generalize the "Self-dual" action, is then proposed. It is obtained by sewing local self-dual theories. Its global equivalence to the Topological Massive gauge theory is shown. UNIVERSIDAD SIMON BOLIVAR

Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models:the string in self-interaction through a Kalb-Ramond field in four dimensions, the topological interaction of two particles due to a BF term in 2+1 dimensions, and the string-particle interaction mediated by a BF term in 3 + 1 dimensions. In the first case one finds that a consistent "surfacerepresentation" can be built provided that the coupling constant is quantized. The geometrical setting that arises corresponds to a generalized version of the Faraday's lines picture: quantum states are labeled by the shape of the string, from which emanate "Faraday's surfaces". In the other models, the topological interaction can also be described by geometrical means. It is shown that the open-path (or open-surface) dependence carried by the wave functional in these models can be eliminated through an unitary transformation, except by a remaining dependence on the boundary of the path (or surface). These feature is closely related to the presence of anomalous statistics in the 2 + 1 model, and to a generalized "anyonic behavior" of the string in the other case.