The equations of quantum as well as classical mechanics are time-reversible if there is no variable in time or magnetic external fields. In contrast to other discrete symmetries, this symmetry does not correspond to any conserved Hermitian operator. Under time reversal, not only do operators of linear and angular momenta have to change sign but the direction of processes has to be reversed as well. A final state of a particle with momentum p and spin s is to be transformed into the initial state of the time-reversed process with momentum −p and spin −s. Therefore the time reversal operation T includes transposition (or complex conjugation K) of observables.
Let us define the time reversal operation as