  In this dissertation the Weyl-Wigner approach is presented as a map between
functions on a real cartesian symplectic vector space and a set of operators on
a Hilbert space, to analyse some aspects of the relations between quantum and
classical formalism, both as a quantization, and as a classical limit. It is
presented an extension of this formalism to the case of a more general
classical phase space, namely one whose configuration space is a compact simple
Lie group. In the second part, it is used to develop a fuzzy approximation to
the algebra of functions on a disc. This is the first example of a fuzzy space
originating from a classical space which has a boundary. It is analysed how
this approximation copes the presence of ultraviolet divergences even in
noninteracting field theories on a disc.
