五维Minkowski空间中非齐次de Sitter群和方程的表示
On representations of the inhomogeneous de Sitter group and equations in five-dimensional Minkowski space
摘要：
本文是我们的简讯quant-ph/0206057（Nucl. Phys. B，1968，7，79）的继续和详细阐述，其中提出了变质量问题的一些方法。在这里我们找到了非齐次群P（1，n）的不可约表示的两类确定实现（当P_0^2-P_k^2>0和P_0^2-P_k^2<0时），非齐次群P（1，n）是（1+n）维Minkowski空间中的平移和旋转群。所有的P（1，n）-不变方程的薛定谔-Foldy型写下来。讨论了基于非齐次deSitter群P（1，4）的量子方案的物理解释方程。对P（1，4）格式下的Dirac和Kemmer-Duffin型方程进行了分析。得到了与该方程有关的代数P（1，4）的表示的具体实现.发现在Kemmer-Duffin型方程的P（1，4）格式中，描述了一个类似于核子-反核子的费米子多重态。
英文摘要：
This paper is a continuation and elaboration of our brief notice quant-ph/0206057 (Nucl. Phys. B, 1968, 7, 79) where some approach to the variable-mass problem was proposed. Here we have found a definite realization of irreducible representations of the inhomogeneous group P(1,n), the group of translations and rotations in (1+n)-dimensional Minkowski space, in two classes (when P_0^2-P_k^2>0 and P_0^2-P_k^2<0). All P(1,n)-invariant equations of the Schrodinger-Foldy type are written down. Some equations of physical interpretation of the quantal scheme based on the inhomogeneous de Sitter group P(1,4) are discussed. The analysis of the Dirac and Kemmer-Duffin type equations in the P(1,4) scheme is carried out. A concrete realization of representations of the algebra P(1,4) connected with this equations, is obtained. The transformations of the Foldy-Wouthuysen type for this equations are found. It is shown that in the P(1,4) scheme of the Kemmer-Duffin type equation describes a fermion multiplet like the nucleon-antinucleon.
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