标题： 非对易时空中的量子粒子：一种身份危机 显示英文标题

标题： Quantum particles in non-commutative space-time: an identity crisis

摘要： 我们认为，在由时空对称性的非交换变形所支配的量子系统中，相同粒子的概念不再有明确的定义。 这类模型的特点是四动量空间由一个非阿贝尔李群给出。 我们的分析基于这样一个观察：对于包含多个粒子的状态，只有系统的总动量是一个明确的量子数。 这种总动量是从粒子个体动量的非阿贝尔组合得到的，而这些个体动量已不再唯一确定。 我们分析的主要结论是，所有之前试图为这些模型构建福克空间的努力都建立在错误的假设上，并且确实已经失败。 我们还展示了动量量子数的自然编织特性，这种特性表征了态张量积中因子的交换，并且在相对论变换下是协变的，从而解决了该领域长期存在的一个问题。 显示英文摘要

摘要： We argue that the notion of identical particles is no longer well defined in quantum systems governed by non-commutative deformations of space-time symmetries. Such models are characterized by four-momentum space given by a non-abelian Lie group. Our analysis is based on the observation that, for states containing more than one particle, only the total momentum of the system is a well defined quantum number. Such total momentum is obtained from the non-abelian composition of the particles individual momenta which are no longer uniquely defined. The main upshot of our analysis is that all previous attempts to construct Fock spaces for these models rested on wrong assumptions and indeed have been unsuccessful. We also show how the natural braiding of momentum quantum numbers which characterizes the exchange of factors in the tensor product of states is covariant under relativistic transformations thus solving a long standing problem in the field.