Many-particle states time reversal

We now consider the effect of time reversal on a general many-particle state (determinant), which we write in terms of A and B strings ... 

Because of the difference in the nature of holes and particles, we need to pay special attention to the possible spin states of the entire system. When the electron is removed from state " (r - R ), the many-body state has a total spin z-component = -Sh, since the original ground state had spin 0. Therefore, the new state created by adding a particle in state - R ) produces a many-body state with total spin z-component S = Sp — Sh. This reveals that when we deal with hole states, we must take their contribution to the spin as the opposite of what a normal particle would contribute. Taking into consideration the fact that the hole has opposite wave-vector of a particle in the same state, we conclude that the hole corresponds to the time-reversed particle state, since the effect of the time-reversal operator T on the energy and the wavefunction is ... 

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