Non-Abelian and Abelian Symmetry Groups Containing Time-Reversal Operators

  • Ion I. GeruEmail author
Part of the Springer Tracts in Modern Physics book series (STMP, volume 281)


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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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute of ChemistryAcademy of Sciences of MoldovaChisinauMoldova

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