Abstract
On the basis of the group-theoretic approach, the existence of six new time reversal operators is proved, along with the well-known anti-unitary time-reversal operator introduced into quantum mechanics by Wigner. Among the new time-reversal operators, three are anti-unitary and three are unitary. A characteristic feature of the new time-reversal operators is that under their action the signs do not change for all three spin projection operators, but only for two or only for one of them. For this reason, such operators should be called operators of incomplete time reversal, in contrast to the Wigner operator, which in this context is an operator of complete time reversal.
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- 1.
In [409], a geometric proof of the Kramers theorem was obtained for the case of a particle with the spin 1/2 based on the \(4'm'm\) group of generalized symmetry of a square with neighboring vertices colored in different colors (at the same color of opposite vertices). The group \(4'm'm\) is isomorphic to the eighth-order group \(G_8\) containing the time-reversal operator, on the basis of which it would be possible to prove the existence of incomplete time-reversal operators. However, in [409] this was not done.
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Geru, I.I. (2018). Non-Abelian and Abelian Symmetry Groups Containing Time-Reversal Operators. In: Time-Reversal Symmetry. Springer Tracts in Modern Physics, vol 281. Springer, Cham. https://doi.org/10.1007/978-3-030-01210-6_8
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DOI: https://doi.org/10.1007/978-3-030-01210-6_8
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