  We review the way to analytically continue the Lippmann-Schwinger bras and
kets into the complex plane. We will see that a naive analytic continuation
leads to nonsensical results in resonance theory, and we will explain how the
non-obvious but correct analytical continuation is done. We will see that the
physical basis for the non-obvious but correct analytic continuation lies in
the invariance of the Hamiltonian under anti-unitary symmetries such as time
reversal or PT.
