Time Reversal for Spacetime and Internal Symmetry
The standard time reversal transformations have to be generalized when we deal with systems with internal symmetry. This generalization is formulated and adapted to higher symmetries involving the angular momentum.
Time reversal in quantum mechanics is a discrete transformation which associates with each motion a “time reversed motion” determined kinematically. When the reversed motion obeys the same equations of motion as the direct equations we state that there is time reversal invariance. Since the choice of the time origin is arbitrary, time reversal invariance automatically implies time translation invariance, whether it is reversible or irreversible.
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