  In this thesis I studied the Symanzik's method for the introduction of the
boundary in a field theory and, specifically, I applied this method to three
Topological Field Theories of the Shwartz type: the non-abelian Chern-Simons
model, the non-abelian three-dimensional BF theory and its abelian
four-dimensional version. This thesis is organized into three chapters. In
Chapter 1 the introduction of the boundary in the non-abelian CS model is
illustrated. The purpose of this chapter is to describe some techniques known
in literature, which are largely used in the following chapters. In Chapter 2
the three-dimensional non-abelian BF theory with a boundary is analyzed. The
most interesting result of this chapter is the interpretation of the boundary
term of the Ward Identities as the gauge-fixing for the residual gauge
invariance of the theory on the boundary. In Chapter 3 the techniques developed
in the previous chapters are applied to the abelian BF theory in four
space-time dimensions with a boundary. The most interesting result of this
chapter, (and of the entire thesis), is the characterization of the boundary
dynamics in terms of canonical commutation relations generated by the algebra
of local boundary observables, which exists due to the residual gauge
invariance of the bulk theory. The results obtained suggest that this model can
be considered as an effective theory for the (3+1)D Topological Insulators.
