A Class of Nonlinear Realizations of the Poincaré Group
A Class of Nonlinear Realizations of the Poincaré Group
复制标题
庞加莱群的一类非线性实现
DOI：
10.1063/1.1665970
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发表时间：
1972
期刊：
影响因子：
--
通讯作者：
A. Albano
中科院分区：
文献类型：
--
作者：
M. Dresden;A. Albano
展示了一类非线性时空变换，它形成了庞加莱群的非线性实现。变换使得表达式I = x2+f（xμ/x 0）不变; f是比率xμ/x 0的任意函数。无穷小生成元被构造为Minkowski空间中的微分算子。这些变换仅定义在闵可夫斯基空间的限制区域A（允许区域）中。通过引入辅助变量，这些变换可以被改写成它们通常的线性形式;然而，这一般只可能在不同于A的区域L（线性区域）中。对函数f的一种特殊形式，给出了区域结构的一般分析和显式表示。在非线性形式主义所提出的物理思想中，有一个概念是“符合的相对性”。这表达了这样一个事实，即在一个参考系中重合（或具有任意小的闵可夫斯基分离）的事件将不会重合（或将具有有限的时间间隔）。
A class of nonlinear space‐time transformations is exhibited, which forms a nonlinear realization of the Poincare group. The transformations leave the expression I = x2+f(xμ/x0) invariant; f is an arbitrary function of the ratios xμ/x0. The infinitesimal generators are constructed as differential operators in the Minkowski space. The transformations are defined only in a restricted region A (the allowed region) of the Minkowski space. By introducing auxiliary variables, the transformations can be recast in their usual linear form; this, however, is in general possible only in a region L (the linear region) which is different from A. The region structure is analyzed in general and given explicitly for a special form of the function f. Among the physical ideas suggested by the nonlinear formalism is the notion of ``relativity of coincidence.'' This expresses the fact that events coincident (or having arbitrary small Minkowski separation) in one frame of reference will not be coincident (or will have finite ...