We study the consequences of the existence of a one-parameter group of conformal motions for anisotropic matter, in the context of general relativity. It is shown that for a class of conformal motions (special conformal motions), the equation of state is uniquely determined by the Einstein equations. For spherically symmetric and static distributions of matter we found two analytical solutions of the Einstein equations which correspond to isotropic and anisotropic matter, respectively. Both solutions can be matched to the Schwarzschild exterior metric and possesses positive energy density larger than the stresses, everywhere within the sphere.

The loop representation formulation of nonrelativistic particles coupled with Abelian gauge fields is studied. Both Maxwell and Chern-Simons interactions are separately considered. It is found that the loop-space formulations of these models share significant similarities, although in the Chern-Simons case there exists a unitary transformation that allows us to remove the degrees of freedom associated with the paths. The existence of this transformation, which allows us to make contact with the anyonic interpretation of the model, is subjected to the fact that the charge of the particles is quantized. On the other hand, in the Maxwell case, we find that charge quantization is necessary in order for the geometric representation to be consistent.

The Proca model is quantized in an open-path dependent representation that generalizes the Loop Representation of gauge theories. The starting point is a gauge invariant Lagrangian that reduces to the Proca Lagrangian when certain gauge is selected. *

We study a generalization of the group of loops that is based on sets of signed points, instead of paths or loops. This geometrical setting incorporates the kinematical constraints of the Sigma Model, inasmuch as the group of loops does with the Bianchi identities of Yang-Mills theories. We employ an Abelian version of this construction to quantize the Self-Dual Model, which allows us to relate this theory with that of a massless scalar field obeying nontrivial boundary conditions.