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 in such a way that 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.
