相对论不变质量算符
A relativistically invariant mass operator
摘要：
在乌克兰。《物理学杂志》，1967，V.12，N 5，p.741-746中示出了对于给定的基本粒子或假设粒子的（离散）质量谱，可以构造一个包含庞加莱代数P作为子代数的非平凡代数G，使得质量算子，定义在给定不可约表示G之一的整个空间中，是自共轭的，其光谱与给定的质谱一致。这种代数是在非相对论情况下以显式形式构造的，即，生成器是为代数写的。然而，在相对论情形下如何构造性地指定代数G和确定质量算符的显式形式的问题仍然没有解决。在目前的工作中，我们提出了这个问题的解决方案，构造连续类似的经典代数U（N）和SP（2 N），并表明，包括庞加莱代数的问题可以制定的语言波函数方程。
英文摘要：
In Ukrain. J. Phys., 1967, V.12, N 5, p.741-746 it was shown how, for a given (discrete) mass spectrum of elementary or hypothetical particles, it was possible to construct a non-trivial algebra G containing a Poincare algebra P as a subalgebra so that the mass operator, defined throughout the space where one of the irreducible representations G is given, is self-conjugate and its spectrum coincides with the given mass spectrum. Such an algebra was constructed in explicit form for the nonrelativistic case, i.e., the generators were written for the algebra. However, the problem of how to assign the algebra G constructively and determine an explicit form of the mass operator in the relativistic case has remained unsolved. In the present work we present a solution of this problem, construct continuum analogs of the classical algebras U(N) and Sp(2N), and show that the problem of including the Poincare algebra can be formulated in the language of wave function equations.
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