Conformal field theories comprise a vast class of exactly solvable two dimensional quantum field theories. Conformal theories with an enlarged symmetry group, the current algebra symmetry, axe a key ingredient to possible string compactification models. The following work explores a Lagrangian approach to these theories. In the first part of this thesis, a large class of conformal theories, the so-called coset models, are derived semi-classically from a gauged version Of the Wess-Zumino-Witten functional. A non-local field transformation to the parafermionic field description is employed in the quantization procedure. Classically, these parafermionic fields satisfy non-trivial Poisson brackets, providing insight into the fractional spin nature of the conformal theory. The W-algebra symmetry is shown to appear naturally in this approach. In the second part of this thesis, the connection between the fusion algebra structure of Wess-Zumino-Witten models and the quantization of the Chern-Simons action on the torus is made explicit. The modular properties of the conformal model are also derived in this context, giving a natural demonstration of the Verlinde conjecture. The effects of background gauge fields and monopoles are also discussed.

Many areas of research rely on the detection of radiation, in the form of single photons or particles. By measuring the photons or particles coming from an object a lot can be learned about the object under study. In some cases there is a simple need to know the number of photons coming from the source. In cases like this a simple counter, like a Geiger-Mueller survey meter, will suffice. In other cases one want to know the spectral distribution of the photons coming from the source. In cases like that a spectrometer is needed that can distinguish between photons with different energies, like a diffraction or transmission grating. The work presented in this thesis focused on the development of a new generation broad band spectrometer that has a high energy resolving power, combined with a high absorption efficiency for photon energies above 10 keV and up to 500 keV. The spectrometers we are developing are based on low-temperature sensors, like superconducting tunnel junctions or transition edge sensors, that are coupled to bulk absorber crystals. We use the low-temperature sensors because they can offer a significant improvement in energy resolving power, compared to conventional spectrometers. We couple the low-temperature sensors …