© 2018

Time-Reversal Symmetry

Seven Time-Reversal Operators for Spin Containing Systems


Part of the Springer Tracts in Modern Physics book series (STMP, volume 281)

About this book


This book introduces new developments in the field of Time-Reversal Symmetry presenting, for the first time, the Wigner time-reversal operator in the form of a product of two- or three time-reversal operators of lower symmetry. The action of these operators leads to the sign change of only one or two angular momentum components, not of all of them. It demonstrates that there are six modes of time-reversal symmetry breaking that do not lead to the complete disappearance of the symmetry but to its lowering. The full restoration of the time-reversal symmetry in the six cases mentioned is possible by introducing six types of metaparticles. The book also confirms the presence of six additional time-reversal operators using a group-theoretical method. The problem is only where to seek these metaparticles. 

The book discusses time-reversal symmetry in classical mechanics, classical and relativistic electrodynamics, quantum mechanics and theory of quantized fields, including dynamical reversibility and statistical irreversibility of the time, Wigner’s and Herring’s criteria, Kramers theorem, selection rules due to time-reversal symmetry, Onsager’s relations, Poincaré recurrence theorem, and CPT theorem. It particularly focuses attention on time-reversal symmetry violation. It is proposed a new method of testing the time-reversal symmetry, which is confirmed experimentally by EPR spectroscopy data. 

It shows that the traditional black-white point groups of magnetic symmetry are not applicable to magnetic systems with Kramers degeneration of energy levels and that magnetic groups of four-color symmetry are adequate for them. Further, it addresses the predicted structural distortions in Kramers three-homonuclear magnetic clusters due to time-reversal symmetry that have been identified experimentally. 

Lastly, it proposes a method of synthesis of two-nuclear coordination compounds with predictable magnetic properties, based on the application of the time-reversal transformation that was confirmed experimentally.


Wigner Time-Reversal Symmetry Wigner Time-Reversal Operator Non-Wigner Time-Reversal Operators Factorization of Wigner Time-Reversal Operator Four-Color Groups of Magnetic Symmetry Magnetic Properties of Binuclear Clusters Non-Kramers Degeneracy

Authors and affiliations

  1. 1.Institute of ChemistryAcademy of Sciences of MoldovaChisinauMoldova

About the authors

Prof. Ion I. Geru got the PhD degree in 1967. In 1986, he became professor of theoretical physics, State University of Moldova. In 1996–1997, he was head of the Department of General Physics. In the years 2005–2008, he was director of the National Center for Analytical Methods and Metrology of the Academy of Sciences of Moldova. In 2008-2013, he was head of the Laboratory “Magnetic Resonance and Laser Spectroscopy”, Center of Chemical Physics and Nanocomposites, Institute of Chemistry of the Academy of Sciences of Moldova. Currently, he is Chief Researcher at the same Institute. 

In the years 2004–2007, Prof. Geru was a part-time visiting professor at the Florida State University. Since 2000, he is a Corresponding Member of the Academy of Sciences of Moldova. In 1998-2017, he was member of the AMPERE Committee. Since 1984, he is the Vice-President of the Moldovan Physical Society. He has more than 330 publications and 4 books, including I. Geru, D. Suter, Resonance Effects of Excitons and Electrons: Basics and Applications, Springer-Verlag, 2013.

Bibliographic information


“The present book is a wonderful explanation of this subject. The book begins with basic facts but mostly is devoted to the modern theory. It is to mention that experimental confirmation are also discussed in details.” (Dmitry Artamonov, zbMath 1412.81005, 2019)