Time-reversal symmetry. Seven time-reversal operators for spin containing systems
The time reversal symmetry in the classical or relativistic (non-quantum) mechanics seems to be a trivial symmetry of the equations of motions. Essentially the only it's interesting consequence in the energy conservation law. Nevertheless in the quantum case the situation changes drastically. In particular in magnetic systems the presence of this symmetry leads to numerous non-trivial consequences. 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. In Chapter 1 the time reversal symmetry in classical and relativistic mechanics is discussed. In Chapter 2 the time reversal symmetry in the framework of the quantum mechanics and the quantum field theory is considered. The main subjects of this chapter are the Wigner (for atomic spectra) and Herring criteria (for crystals). for the energy level degeneracy due to the time reversal symmetry. Also the Kramers and the CPT theorems are explained in details. Chapter 3 is devoted to magnetic symmetry groups. It is presented the following method of construction of these groups: an extension of 32 point symmetry group using a cyclic group of the second order containing the time reversal symmetry operator. It is shown that this method works only in the case of the so called non-Kramers systems. In the latter case the extension must be done using a cyclic group of the fourth order. In Chapter 4 anomalous properties of trihomonuclear Kramers systems due to the symmetry obtained above are considered. In Chapter 5 the time reversal symmetry for quantum systems with quasienergy spectrum is considered. In Chapter 6 an original method is proposed for converting antiferromagnetic-type exchange interaction into ferromagnetic and vice versa in magnetic dimer cluster. The construction of this transformation is based on a usage of the time reversal transformation. Also in this chapter an experimental confirmation of the method is given. In Chapter 7 an instability of spin populations in Kramer's clusters is discussed. In Chapters 8,9 a factorization of the time reversal operator is constructed. The complete time reversal operator is represented as a product of two or three operators (called incomplete time reversal operators). Commutation relations between these operators are found. They are different for Kramers and non-Kramers systems. The angular momentum operator \(J\) can be represented as a sum of the boson occupation numbers, these numbers can be negative. This situation is interpreted as a presence of anti-boson states, which can be obtained from boson states by the action of the time reversal operator. By analogy the constructed incomplete time reversal operator leads to the construction of meta particles. These meta particles are also discussed in Chapter 9. In Chapter 10 an experimental method for testing breaking of the time reversal symmetry is discussed.
scientific article; zbMATH DE number 6968469