We propose for the spin density matrix two parametrizations which automatically fulfill the non-negativity conditions, without setting any bound on the parameters. The first one relies on a theorem, that we prove, and it is rather simple and easily adaptable to some specific reactions, where, for example, parity is conserved or angular momentum conservation entails selection rules. Moreover, in the case when the rank is less than the order of the density matrix, we show how to improve the fits to the data, either by implementing previous suggestions, or by elaborating an alternative method, for which we prove a second theorem. Our second parametrization is a variant of previous treatments, it appears suitable for some particular processes. Moreover, we discuss about the possibility of inferring the elements of the density matrix from the differential decay width. Last, we illustrate various examples of current interest, both in strong and weak decays; some of them may be helpful in the investigation of physics beyond the standard model.

我们为自旋密度矩阵提出了两个参数化参数，它们可以自动满足非负条件，而无需在参数上设置任何限制。第一个依赖于我们证明的一个定理，它相当简单并且易于适应某些特定的反应，例如，保持奇偶性或角动量守恒需要选择规则。此外，在等级小于密度矩阵的阶数的情况下，我们展示了如何通过实施先前的建议或阐述替代方法来改善对数据的拟合，为此我们证明了第二个定理。我们的第二个参数化是先前处理的一种变体，它似乎适用于某些特定过程。而且，我们讨论从微分衰减宽度推断密度矩阵元素的可能性。最后，我们以强衰减和弱衰减为例，说明了当前关注的各种示例。其中一些可能对标准模型以外的物理研究很有帮助。