TITLE:
Scaling Transformation for Nonlocal Interactions
AUTHORS:
Hai-Jun Wang
KEYWORDS:
Scaling Transformation, Renormalization, Conservation Law, Spin Crisis, Nonlocal Scattering
JOURNAL NAME:
Journal of Modern Physics,
Vol.6 No.5,
April
28,
2015
ABSTRACT: 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. The nonlocal
interaction Lagrangian turns out to vary under scaling transformation,
analogous to running cases in renormalization. And the total Lagrangian becomes
scale invariant only under some extreme conditions. The conservation law of
this extreme Lagrangian is discussed and a contribution named scalum appears to
the spin angular momentum. Finally a mechanism is designed to test the scaling
effect on nonlocal interaction.