Derivatives with Twists

We described the twisted interval above in terms of pure mathematics; yet twisting plays several roles in physics. First, one often encounters parallel transport about a closed trajectory. The physical role of twisting includes the fact that the condition (2) ensures that angular momentum zero is not allowed, 0 6∈ K. Hence twisting provides an infra-red regularization, which can be useful in the study of massless fields. In fact, this author has taken advantage of these properties in recent works, see [1, 2, 3] and other works cited there. These investigations led to the genesis of the current paper, for in the detailed estimates one must compare different twists. This comparison can be carried out using the bounds that we establish here.