Exact Results in Quantum Theory

Loop Quantum Gravity is one of the most prominent examples of a quantum theory where elementary variables are polymerlike, i.e. supported on submanifolds of lower dimension than the space manifold of a theory. Therefore similar background independent framework of quantization was needed to matter fields, e.g. scalar field. At first momentum space representation for scalar field was provided in which operators corresponding to momenta are diagonal and field operators exist only in the exponentiated form. Later the modification of this framework, i.e. position space representation was used to address the issue of quantum resolution of black hole singularities in the spherically symmetric part of gravitational phase space. In this talk the generalization of these frameworks to real vector fields will be presented.