Documentation does not specify basis choice when discrete symmetries are declared
The documentation does not specify which basis is used for the scattering states when discrete symmetries are declared, with or without a conservation law. This can easily be confusing, especially because for a given discrete symmetry, we use different bases depending on whether a conservation law is present or not.
For example, with time reversal \mathcal{T}
alone, each outgoing mode is chosen as a time-reversed partner of an incoming mode, i.e. \psi_{out} = \mathcal{T} \psi_{in}
. But assuming we have a spin conservation law -\sigma_z
together with \mathcal{T}
, the spin down modes are chosen as the time-reversed partners of the incoming modes, i.e.
\psi_{out}^\downarrow = \mathcal{T}\psi_{in}^\uparrow
and \psi_{in}^\downarrow = \mathcal{T}\psi_{out}^\uparrow
, and thus \psi_{out} \neq \mathcal{T} \psi_{in}
.