标题： 非厄米特${\cal PT}$-对称的强磁场中的相对论量子理论 显示英文标题

标题： Non-Hermitian ${\cal PT}$-symmetric relativistic quantum theory in an intensive magnetic field

摘要： 我们发展相对论非厄米量子理论及其在强磁场中中微子物理中的应用。 众所周知，量子理论的基本假设之一是物理参数的厄米性要求。 这一条件不仅保证了哈密顿算符本征值的实性，还意味着所考虑的量子过程的概率保持不变。 然而，正如相对较近所显示的（Bender, Boettcher 1998），厄米性是一个充分条件，但不是必要条件。 结果表明，在非厄米哈密顿量中可以选出一些具有实数能谱并且能够确保系统随时间演化并保持幺正性的哈密顿量。 这种类型的哈密顿量包括所谓的宇称-时间（${\cal PT}$）对称模型，该模型已在现代物理学的各个领域得到应用。 在这方面，最成熟的是用于${\cal PT}$-对称光学领域的模型，多年来不仅进行了理论研究，还进行了实验研究。 显示英文摘要

摘要： We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of physical parameters. This condition not only guarantees the reality of the eigenvalues of Hamiltonian operators, but also implies the preservation of the probabilities of the considered quantum processes. However as it was shown relatively recently (Bender, Boettcher 1998), Hermiticity is a sufficient but it is not a necessary condition. It turned out that among non-Hermitian Hamiltonians it is possible to allocate a number of such which have real energy spectra and can ensure the development of systems over time with preserving unitarity. This type of Hamiltonians includes so-called parity-time (${\cal PT}$) symmetric models which is already used in various fields of modern physics. The most developed in this respect are models, which used in the field of ${\cal PT}$-symmetric optics, where for several years produced not only theoretical but experimental studies.