Wightman框架中描述相互作用理论的一个准则
A criterion to characterize interacting theories in the Wightman framework
摘要：
在相对论量子场论的适当Wightman框架下，提出了一个刻画相互作用理论的判据，该判据包含了一个“奇点假设”，这个“奇点假设”已经被证明了很长时间，并得到了重整化群理论的支持，但从未得到数学上的表述.在这些理论中发生的（非微扰）波函数重整化$Z$不一定等于零，除非假设等时对易关系（ETCR）。由于ETCR在一般情况下是不合理的（因为相互作用场一般不能被限制在尖锐的时间，正如从模型研究中所知道的那样），条件$Z=0$在相互作用理论中不是普遍有效的。我们推测，它的特点是不稳定的（复合）粒子或带电粒子，成为infroparticles在无质量粒子的存在。在QED的情况下，这样的“修饰”电子预计不会被限制，但在QCD中，我们提出了一个夸克限制标准，它自然地遵循由Casher，Kogut和Susskind以及Lowenstein和Swieca的工作所建议的线。
英文摘要：
We propose a criterion to characterize interacting theories in a suitable Wightman framework of relativistic quantum field theories which incorporates a "singularity hypothesis", which has been conjectured for a long time, is supported by renormalization group theory, but has never been formulated mathematically. The (nonperturbative) wave function renormalization $Z$ occurring in these theories is shown not to be necessarily equal to zero, except if the equal time commutation relations (ETCR) are assumed. Since the ETCR are not justified in general (because the interacting fields cannot in general be restricted to sharp times, as is known from model studies), the condition $Z=0$ is not of general validity in interacting theories. We conjecture that it characterizes either unstable (composite) particles or the charge-carrying particles, which become infraparticles in the presence of massless particles. In the case of QED, such "dressed" electrons are not expected to be confined, but in QCD we propose a quark confinement criterion, which follows naturally from lines suggested by the works of Casher, Kogut and Susskind and Lowenstein and Swieca.
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