呼吸相对论旋转体与基本动力系统
Breathing Relativistic Rotators and Fundamental Dynamical Systems
摘要：
最近的研究表明，Kuzenko，Lyakhovich和Segal在1994年提出的大质量自旋粒子的力学模型，也就是Staruszkiewicz在15年后在完全不同的背景下独立地重新发现的基本相对论性旋转体，作为一个动力学系统是有缺陷的，即它的Cauchy问题是不好定的。这个动力学系统是基本的，因为它的质量和自旋是参数，而不是任意的运动常数，这是量子不可约性的经典对应物。因此，希望找到其他对象，除了是基本的，也会很好地提出柯西问题。为此，一类呼吸旋转器被认为是。呼吸旋转体由与位置相关的单个零矢量组成，并根据某些相对论运动定律运动。令人惊讶的是，呼吸旋转器是基本的，也是有缺陷的动力系统。更一般地说，它已被证明，呼吸转子是类似的缺陷的必要条件，是其庞加莱{é}群的卡西米尔不变量的功能依赖。
英文摘要：
Recently, it was shown, that the mechanical model of a massive spinning particle proposed by Kuzenko, Lyakhovich and Segal in 1994, which is also the fundamental relativistic rotator rediscovered independently 15 years later by Staruszkiewicz in quite a different context, is defective as a dynamical system, that is, its Cauchy problem is not well posed. This dynamical system is fundamental, since its mass and spin are parameters, not arbitrary constants of motion, which is a classical counterpart of quantum irreducibility. It is therefore desirable to find other objects which, apart from being fundamental, would also have well posed Cauchy problem. For that purpose, a class of breathing rotators is considered. A breathing rotator consists of a single null vector associated with position and moves in accordance with some relativistic laws of motion. Surprisingly, breathing rotators which are fundamental, are also defective as dynamical systems. More generally, it has been shown, that the necessary condition for a breathing rotator to be similarly defective, is functional dependence of its Casimir invariants of the Poincar{é} group.
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