Scaling Transformation for Nonlocal Interactions

Understand

In the light of their relationships with renormalization, in this paper we associate the scaling transformation with nonlocal interactions.

• On one hand, the association leads us to interpret the nonlocality with locally symmetric method.
• On the other hand, we find that the nonlocal interaction between hadrons could be test ground for scaling transformation if ascribing the running effects in renormalization to scaling transformation.
• First we derive directly from group theory the operator/coordinate representation and unitary/spinor representation for scaling transformation, then link them together by inquiring a scaling-invariant interaction vertex mimicking the similar process of Lorentz transformation applied to Dirac equation.