Wave maps e l'approccio algebrico alla teoria dei campi classica

The aim of this thesis is twofold: on one hand we study the Cauchy problem associated with the theory of wave maps, on the other we describe an analytic procedure that, given a Lagrangian over some fiber bundle, which we assume has normally hyperbolic linearized dynamical equations, allow us to implement the structure of Poisson *-algebra for microcausal functionals, via the Peierls bracket. Furthermore we will establish a suitable topology and then examine properties of such algebra.