  We analyse the effects of Robin boundary conditions on quantum field theories
of spin 0, 1 and 1/2. In particular, we show that these conditions always lead
to the appearance of edge states that play a significant role in quantum Hall
effect and topological insulators. We prove in a rigorous way the existence of
spectral lower bounds on the kinetic term of the Hamiltonian, which guarantees
the stability and consistency of massive field theories when the mass is larger
than the lower bound of the kinetic term. We also find an upper bound for the
deepest edge state. The explicit dependence of both bounds on the boundary
conditions and the size of the system is derived under very general conditions.
For fermionic systems we analyse the case of Atiyah-Patodi-Singer and chiral
bag boundary conditions. We point out the existence of edge states also in
these cases and show that they disappear for small enough systems. Stability is
granted in this case.
