Exact Results in Quantum Theory

I will give an introduction to integral quantizations, with stress on the quantization of a particle in 1 dimension in terms of coherent states of Heisenberg group. The same formalism will then be applied to the quantization of homogeneous isotropic cosmology (the only difference being the replacement of Heisenberg group with the Affine group). I will show how this simple procedure leads to a quantum theory in which the initial Big Bang singularity is removed, and how the semiclassical limit can be naturally estracted.